Apparatus, system, and method for determining the degradation of an SCR catalyst

ABSTRACT

According to one representative embodiment, an apparatus for determining the degradation of a selective catalytic reduction (SCR) catalyst of an engine exhaust aftertreatment system includes a system properties module configured to store at least one system dynamics property value of the exhaust system at a first time and receive the at least one system dynamics property value of the exhaust aftertreatment system at a second time subsequent to the first time. The apparatus also includes a system dynamics module configured to determine a storage capacity of the SCR catalyst based on a comparison between the at least one system dynamic property value at the first time and the at least one system dynamic property value at the second time. Additionally, the apparatus includes an SCR catalyst degradation factor module configured to determine an SCR catalyst degradation factor based at least partially on the storage capacity of the SCR catalyst.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Patent Application No. 61/120,283, filed Dec. 5, 2008, and is a continuation-in-part application of U.S. patent application Ser. No. 12/112,500, filed Apr. 30, 2008, U.S. patent application Ser. No. 12/112,622, filed Apr. 30, 2008, U.S. patent application Ser. No. 12/112,678, filed Apr. 30, 2008, and U.S. patent application Ser. No. 12/112,795, filed Apr. 30, 2008. These applications are incorporated herein by reference.

FIELD

This disclosure relates to an exhaust aftertreatment system having an SCR catalyst, and more particularly to apparatus, systems and methods for determining a degradation factor of the SCR catalyst.

BACKGROUND

Emissions regulations for internal combustion engines have become more stringent over recent years. The regulated emissions of NO_(x) and particulates from internal combustion engines are low enough that in many cases the emissions levels cannot be met with improved combustion technologies. Therefore, the use of exhaust aftertreatment systems on engines to reduce emissions is increasing.

Some exhaust aftertreatment systems include particulate matter filters for controlling or reducing particulate matter emissions and SCR systems for controlling or reducing NO_(x) emissions. SCR systems include NO_(x) reduction catalysts to convert NO_(x) (NO and NO₂ in some fraction) to N₂ and other compounds. SCR systems utilize a reductant, typically ammonia, to reduce the NO_(x). Currently available SCR systems can produce high NO_(x) conversion rates allowing the combustion technologies to focus on power and efficiency. However, currently available SCR systems also suffer from some drawbacks.

Several conditions, including the operation of a particulate matter filter, may negatively affect the operation of an SCR catalyst of an SCR system. For example, operation of a particulate matter filter may lead to fluctuations in the NO to NO₂ ratio entering the SCR catalyst, sulphur fouling of the SCR catalyst, and hydrocarbon accumulation on the SCR catalyst, which can cause a drop in the NO_(x) conversion efficiency and ammonia storage capacity of the SCR catalyst. These conditions are typically reversible by running the engine at a proper operating condition. The operation of a particulate matter filter (e.g., particulate matter filter regeneration events) may also cause thermal degradation of the SCR catalyst. Thermal degradation of the SCR catalyst can lead to a drop in both NO_(x) conversion efficiency and ammonia storage capacity that is not reversible.

Some conventional engine system controllers do not account for the degradation of the SCR catalyst. Therefore, if the SCR catalyst is degraded, the NO_(x) conversion rate commanded by the controller may be too conservative or too aggressive for a given application. Further, for conventional engine system controllers that account for the degradation of the SCR catalyst, such controllers may not account for the affect of degradation on both NO_(x) conversion rates and ammonia storage capacity.

SUMMARY

The subject matter of the present application has been developed in response to the present state of the art, and in particular, in response to the problems and needs in the art that have not yet been fully solved by currently available exhaust aftertreatment systems and associated SCR systems. Accordingly, the subject matter of the present application has been developed to provide apparatus, systems, and methods for determining an SCR catalyst degradation factor that overcomes at least some shortcomings of the prior art SCR systems.

For example, according to one representative embodiment, an apparatus for determining the degradation of a selective catalytic reduction (SCR) catalyst of an engine exhaust aftertreatment system includes a system properties module that is configured to store at least one system dynamics property value of the exhaust system at a first time and receive the at least one system dynamics property value of the exhaust aftertreatment system at a second time subsequent to the first time. The apparatus also includes a system dynamics module that is configured to determine a storage capacity of the SCR catalyst based on a comparison between the at least one system dynamic property value at the first time and the at least one system dynamic property value at the second time. Additionally, the apparatus includes an SCR catalyst degradation factor module that is configured to determine an SCR catalyst degradation factor based at least partially on the storage capacity of the SCR catalyst. In some implementations, the SCR catalyst degradation factor module is configured to determine an ammonia storage capacity SCR catalyst degradation factor and an NO_(x) conversion efficiency SCR catalyst degradation factor based at least partially on the storage capacity of the SCR catalyst.

According to some implementations, the at least one system dynamics property value includes a difference between an SCR catalyst inlet NH₃ signal and an SCR catalyst outlet NO_(x) signal. In certain instances, the at least one system dynamics property value includes a difference between a time constant of an SCR catalyst inlet NH₃ signal and a time constant of an SCR catalyst outlet NO_(x) signal.

In some implementations, the system dynamics module is configured to modulate a parameter of the exhaust aftertreatment system to estimate the parameter value corresponding to at least one system dynamic property of the system. In yet some instances, the system dynamics module is configured to modulate a parameter of the exhaust aftertreatment system at approximately the second time to achieve a parameter value corresponding with the at least one system dynamic property value of the exhaust system at the first time. The modulated parameter can be a urea dosing rate or NO_(x) exiting the engine.

According to certain implementations, the ammonia storage capacity SCR catalyst degradation factor is a first SCR catalyst degradation factor and the NO_(x) conversion efficiency SCR catalyst degradation factor is a second SCR catalyst degradation factor. The SCR catalyst degradation factor module can be configured to determine a third SCR catalyst degradation factor based at least partially on a comparison between at least one predicted SCR catalyst outlet parameter value for a fresh SCR catalyst at given exhaust aftertreatment operating conditions and at least one measured SCR catalyst outlet parameter value for the SCR catalyst at the given exhaust aftertreatment operating conditions. The third SCR catalyst degradation factor can be determined by applying the difference between the at least one predicted SCR catalyst outlet parameter value and the at least one measured SCR catalyst outlet parameter value to a predetermined parameter value difference versus catalyst degradation factor table. In some implementations, the at least one SCR catalyst outlet parameter value includes SCR catalyst outlet NO_(x) and NH₃ values. In such implementations, the SCR catalyst degradation factor module can be configured to determine the predicted SCR catalyst outlet NO_(x) and NH₃ values based at least partially on an SCR catalyst inlet exhaust gas temperature, an SCR catalyst inlet exhaust gas space velocity, an SCR catalyst bed temperature, an SCR catalyst inlet NO_(x) value, an SCR catalyst inlet NO₂/NO_(x) ratio, an SCR catalyst inlet NH₃ value, an SCR catalyst inlet isocyanic acid value, and an SCR catalyst outlet exhaust gas temperature value.

In some implementations of the apparatus, the SCR catalyst degradation module is configured to determine a third SCR catalyst degradation factor based at least partially on an exhaust temperature increase event within the exhaust aftertreatment system. The exhaust temperature increase event can be defined by an exhaust temperature increase amount and an exhaust temperature increase duration where the third SCR catalyst degradation factor is associated with an exhaust temperature increase amount and duration combination.

In a certain implementation, the apparatus includes an ammonia storage capacity module configured to determine a maximum ammonia storage capacity of the SCR catalyst based at least partially on the ammonia storage capacity SCR catalyst degradation factor. Similarly, the apparatus can include an NOx conversion efficiency module configured to determine a maximum NOx conversion efficiency of the SCR catalyst based at least partially on the NO_(x) conversion efficiency SCR catalyst degradation factor.

According to another embodiment, a method for determining the degradation of a selective catalytic reduction (SCR) catalyst of an engine exhaust aftertreatment system includes modulating an SCR catalyst inlet exhaust condition to achieve a predefined SCR catalyst inlet exhaust condition value. The method also includes monitoring an SCR catalyst inlet exhaust condition signal and an SCR catalyst outlet exhaust condition signal and comparing a system dynamics property of the SCR catalyst inlet exhaust condition signal and a corresponding system dynamics property of the SCR catalyst outlet exhaust condition signal. Additionally, the method includes determining a ammonia storage capacity of the SCR catalyst based at least partially on a difference between the system dynamics property of the first SCR catalyst exhaust condition signal and the corresponding system dynamics property of the second SCR catalyst outlet exhaust condition signal. The method further includes determining an SCR catalyst degradation factor based at least partially on the ammonia storage capacity.

In certain implementations of the method, the SCR catalyst degradation factor is an ammonia storage capacity SCR catalyst degradation factor. In yet certain implementations, the method includes correlating the ammonia storage capacity of the SCR catalyst with a NO_(x) conversion efficiency of the SCR catalyst and the SCR catalyst degradation factor is an NO_(x) conversion efficiency SCR catalyst degradation factor.

According to some implementations of the method, the degradation of the SCR catalyst is related to the system dynamics property, which can be a time constant computed using the SCR catalyst inlet exhaust condition signal and the SCR catalyst outlet exhaust condition signal. In certain implementations, the system dynamics property of the SCR catalyst inlet exhaust condition signal is a time constant of the SCR catalyst inlet exhaust condition signal and the system dynamics property of the SCR catalyst outlet exhaust condition signal is a time constant of the SCR catalyst outlet exhaust condition signal.

In yet some implementations, the SCR catalyst inlet exhaust condition includes the amount of NH₃ entering the SCR catalyst. Modulating the amount of NH₃ entering the SCR catalyst can include modulating the flow rate of a reductant injected into the exhaust upstream of the SCR catalyst. The SCR catalyst inlet exhaust sensor signal includes an SCR catalyst inlet NH₃ sensor signal and the SCR catalyst outlet exhaust sensor signal includes an SCR catalyst outlet NO_(x) sensor signal.

According to certain implementations, modulating the flow rate of the reductant injected into the exhaust includes modulating the flow rate to a predefined flow rate corresponding with a given ammonia storage capacity of the SCR catalyst.

In some implementations, the SCR catalyst degradation factor is a first SCR catalyst degradation factor and the method includes determining a second SCR catalyst degradation factor based at least partially on an SCR catalyst inlet exhaust gas temperature, an SCR catalyst inlet exhaust gas space velocity, an SCR catalyst bed temperature, an SCR catalyst inlet NO_(x) value, an SCR catalyst inlet NO₂/NO_(x) ratio, an SCR catalyst inlet NH₃ value, an SCR catalyst inlet isocyanic acid value, and an SCR catalyst outlet exhaust gas temperature value. In certain implementations, a third SCR catalyst degradation factor is determined based at least partially on exhaust temperature increase event information. The method can include determining an overall SCR catalyst degradation factor by combining the first, second, and third SCR catalyst degradation factors.

According to yet another embodiment, an exhaust aftertreatment system configured to receive an exhaust gas stream generated by an internal combustion engine includes a selective catalytic reduction (SCR) catalyst, a reductant doser capable of being in reductant dosing communication with the exhaust gas stream upstream of the SCR catalyst, and an SCR catalyst inlet NH₃ sensor upstream of the SCR catalyst and an SCR catalyst outlet NO_(x) sensor downstream of the SCR catalyst. The exhaust aftertreatment system can also include a controller that is communicable in electronic communication with the reductant doser to command the reductant doser to dose reductant into the exhaust gas stream. The controller includes a system properties modulation module that is configured to modulate an amount of NH₃ entering the SCR catalyst by commanding the reductant doser to inject reductant into the exhaust gas stream at a predefined flow rate. The controller also includes a system properties monitoring module that is configured to monitor an SCR catalyst inlet NH₃ signal generated by the SCR catalyst inlet NH₃ sensor and an SCR catalyst outlet NO_(x) signal generated by the SCR catalyst outlet NO_(x) sensor. Additionally, the controller includes a degradation factor module that is configured to compare a first time constant of the SCR catalyst inlet NH₃ signal and a second time constant of the SCR catalyst outlet NO_(x) signal. The degradation factor module is also configured to determine an SCR catalyst degradation factor based at least partially on a difference between the first and second time constants. Further, the controller includes a reductant doser module that is configured to determine a reductant dosing rate for achieving a desired exhaust emissions reduction based at least partially on the SCR catalyst degradation factor.

In some implementations, the SCR catalyst degradation factor is proportional to the difference between the first and second time constants. In other implementations, the SCR catalyst degradation factor is a non-linear function of the difference between the first and second time constants.

Reference throughout this specification to features, advantages, or similar language does not imply that all of the features and advantages that may be realized with the subject matter of the present disclosure should be or are in any single embodiment. Rather, language referring to the features and advantages is understood to mean that a specific feature, advantage, or characteristic described in connection with an embodiment is included in at least one embodiment of the present disclosure. Thus, discussion of the features and advantages, and similar language, throughout this specification may, but do not necessarily, refer to the same embodiment.

Furthermore, the described features, advantages, and characteristics of the subject matter of the present disclosure may be combined in any suitable manner in one or more embodiments. One skilled in the relevant art will recognize that the subject matter may be practiced without one or more of the specific features or advantages of a particular embodiment. In other instances, additional features and advantages may be recognized in certain embodiments that may not be present in all embodiments. These features and advantages will become more fully apparent from the following description and appended claims, or may be learned by the practice of the subject matter as set forth hereinafter.

BRIEF DESCRIPTION OF THE DRAWINGS

In order that the advantages of the subject matter may be more readily understood, a more particular description of the subject matter briefly described above will be rendered by reference to specific embodiments that are illustrated in the appended drawings. Understanding that these drawings depict only typical embodiments of the subject matter and are not therefore to be considered to be limiting of its scope, the subject matter will be described and explained with additional specificity and detail through the use of the drawings, in which:

FIG. 1 is a schematic block diagram of an internal combustion engine having an exhaust after-treatment system according to one representative embodiment;

FIG. 2 is a schematic block diagram of the exhaust after-treatment system of FIG. 1 according to one representative embodiment;

FIG. 3 is a schematic block diagram of a controller of the exhaust after-treatment system of FIG. 2 according to one representative embodiment;

FIG. 4 is a schematic block diagram of a NO_(x) reduction target module of the controller of FIG. 3 according to one representative embodiment;

FIG. 5A is a schematic block diagram of a feedforward ammonia target module of the controller of FIG. 3 according to one representative embodiment;

FIG. 5B is a schematic block diagram of a feedback ammonia target module of the controller of FIG. 3 according to one representative embodiment;

FIG. 6 is a schematic block diagram of a reductant target module of the controller of FIG. 3 according to one representative embodiment;

FIG. 7 is a schematic block diagram of a reductant hydrolysis module of the reductant target module of FIG. 6 according to one representative embodiment;

FIG. 8 is a schematic block diagram of an inverse reductant hydrolysis module of the reductant target module of FIG. 6 according to one representative embodiment;

FIG. 9 is a schematic flow chart diagram of a control system operable to determine ammonia and isocyanic acid flow into an SCR catalyst according to one embodiment;

FIG. 10 is a schematic block diagram of an ammonia storage module of the controller of FIG. 3 according to one representative embodiment;

FIG. 11 is a schematic block diagram of a current ammonia storage level module of the ammonia storage module of FIG. 10 according to one representative embodiment;

FIG. 12 is a schematic block diagram of an SCR catalyst degradation factor module according to one representative embodiment;

FIG. 13 is a schematic flow chart diagram of a control system operable to determine the storage level of ammonia on an SCR catalyst;

FIG. 14 is a schematic flow chart diagram of a control system operable to determine the amount of ammonia slip from an SCR catalyst;

FIG. 15 is a schematic block diagram of an AMOX catalyst ammonia conversion module of the controller of FIG. 3 according to one representative embodiment;

FIG. 16 is a schematic block diagram of a reductant modifier module of the controller of FIG. 3 according to one representative embodiment;

FIG. 17 is a schematic block diagram of a corrected tailpipe NO_(x) module of the reductant modifier module of FIG. 16 according to one representative embodiment; and

FIG. 18 is a method of reducing NO_(x) emissions using ammonia storage on an SCR catalyst.

DETAILED DESCRIPTION

Many of the functional units described in this specification have been labeled as modules, in order to more particularly emphasize their implementation independence. For example, a module may be implemented as a hardware circuit comprising custom VLSI circuits or gate arrays, off-the-shelf semiconductors such as logic chips, transistors, or other discrete components. A module may also be implemented in programmable hardware devices such as field programmable gate arrays, programmable array logic, programmable logic devices or the like.

Modules may also be implemented in software for execution by various types of processors. An identified module of executable code may, for instance, comprise one or more physical or logical blocks of computer instructions, which may, for instance, be organized as an object, procedure, or function. Nevertheless, the executables of an identified module need not be physically located together, but may comprise disparate instructions stored in different locations which, when joined logically together, comprise the module and achieve the stated purpose for the module.

Indeed, a module of executable code may be a single instruction, or many instructions, and may even be distributed over several different code segments, among different programs, and across several memory devices. Similarly, operational data may be identified and illustrated herein within modules, and may be embodied in any suitable form and organized within any suitable type of data structure. The operational data may be collected as a single data set, or may be distributed over different locations including over different storage devices, and may exist, at least partially, merely as electronic signals on a system or network.

Reference throughout this specification to “one embodiment,” “an embodiment,” or similar language means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, appearances of the phrases “in one embodiment,” “in an embodiment,” and similar language throughout this specification may, but do not necessarily, all refer to the same embodiment.

Furthermore, the described features, structures, or characteristics of the subject matter described herein may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided, such as examples of controls, structures, algorithms, programming, software modules, user selections, network transactions, database queries, database structures, hardware modules, hardware circuits, hardware chips, etc., to provide a thorough understanding of embodiments of the subject matter. One skilled in the relevant art will recognize, however, that the subject matter may be practiced without one or more of the specific details, or with other methods, components, materials, and so forth. In other instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring aspects of the disclosed subject matter.

Internal Combustion Engine System

FIG. 1 depicts one embodiment of an internal combustion engine system 10. The main components of the engine system 10 include an internal combustion engine 11 and an exhaust gas after-treatment system 100 coupled to the engine. The internal combustion engine 11 can be a compression ignited internal combustion engine, such as a diesel fueled engine, or a spark-ignited internal combustion engine, such as a gasoline fueled engine operated lean. The engine system 10 further includes an air inlet 12, intake manifold 14, exhaust manifold 16, turbocharger turbine 18, turbocharger compressor 20, temperature sensors (e.g., temperature sensor 24), pressure sensors (e.g., pressure sensor 26), and air-flow sensor 56. The air inlet 12 is vented to the atmosphere and connected to an inlet of the intake manifold 14 to enable air to enter the intake manifold. The intake manifold 14 includes an outlet operatively coupled to compression chambers of the internal combustion engine 11 for introducing air into the compression chambers.

Within the internal combustion engine 11, the air from the atmosphere is combined with fuel to power the engine. Combustion of the fuel and air produces exhaust gas that is operatively vented to the exhaust manifold 16. From the exhaust manifold 16, a portion of the exhaust gas may be used to power the turbocharger turbine 18. The turbine 18 drives the turbocharger compressor 20, which may compress at least some of the air entering the air inlet 12 before directing it to the intake manifold 14 and into the compression chambers of the engine 11.

The exhaust gas after-treatment system 100 is coupled to the exhaust manifold 16 of the engine 11. At least a portion of the exhaust gas exiting the exhaust manifold 16 can pass through the exhaust after-treatment system 100. In certain implementations, the engine system 10 includes an exhaust gas recirculation (EGR) valve (not shown) configured to open to allow a portion of the exhaust gas to recirculate back into the compression chambers for altering the combustion properties of the engine 11.

Generally, the exhaust gas after-treatment system 100 is configured to remove various chemical compound and particulate emissions present in the exhaust gas received from the exhaust manifold 16 and not recirculated back into the engine 11. As illustrated in FIG. 2, the exhaust gas after-treatment system 100 includes controller 130, oxidation catalyst 140, particulate matter (PM) filter 142, SCR system 150 having an SCR catalyst 152, and ammonia oxidation (AMOX) catalyst 160. In an exhaust flow direction, indicated by directional arrow 144, exhaust may flow from the exhaust manifold 16, through the oxidation catalyst 140, through the particulate filter 142, through the SCR catalyst 152, through the AMOX catalyst 160, and then be expelled into the atmosphere. In other words, the particulate filter 142 is positioned downstream of the oxidation catalyst 140, the SCR catalyst 152 is positioned downstream of the particulate filter 142, and the AMOX catalyst 160 is positioned downstream of the SCR catalyst 152. Generally, exhaust gas treated in the exhaust gas after-treatment system 100 and released into the atmosphere consequently contains significantly fewer pollutants, such as diesel particulate matter, NO_(x), hydrocarbons, such as carbon monoxide and carbon dioxide, than untreated exhaust gas.

The oxidation catalyst 140 can be any of various flow-through, diesel oxidation catalysts (DOC) known in the art. Generally, the oxidation catalyst 140 is configured to oxidize at least some particulate matter, e.g., the soluble organic fraction of soot, in the exhaust and reduce unburned hydrocarbons and CO in the exhaust to less environmentally harmful compounds. For example, the oxidation catalyst 140 may sufficiently reduce the hydrocarbon and CO concentrations in the exhaust to meet the requisite emissions standards.

The particulate filter 142 can be any of various particulate filters known in the art configured to reduce particulate matter concentrations, e.g., soot and ash, in the exhaust gas to meet requisite emission standards. The particulate filter 142 can be electrically coupled to a controller, such as controller 130, that controls various characteristics of the particulate filter, such as, for example, the timing and duration of filter regeneration events. In some implementations, the particulate filter 142 and associated control system is similar to, or the same as, the respective particulate filters and control systems described in U.S. patent application Ser. Nos. 11/227,320; 11/227,403; 11/227,857; and 11/301,998, which are incorporated herein by reference.

The SCR system 150 includes a reductant delivery system 151 that includes a reductant source 170, pump 180 and delivery mechanism 190. The reductant source 170 can be a container or tank capable of retaining a reductant, such as, for example, ammonia (NH₃), urea, diesel fuel, or diesel oil. The reductant source 170 is in reductant supplying communication with the pump 180, which is configured to pump reductant from the reductant source to the delivery mechanism 190. The delivery mechanism 190 can include a reductant injector schematically shown at 192 positioned upstream of the SCR catalyst 152. The injector is selectively controllable to inject reductant directly into the exhaust gas stream prior to entering the SCR catalyst 152. In some embodiments, the reductant can either be ammonia or urea, which decomposes to produce ammonia. As will be described in more detail below, in these embodiments, the ammonia reacts with NO_(x) in the presence of the SCR catalyst 152 to reduce the NO_(x) to less harmful emissions, such as N₂ and H₂O. The SCR catalyst 152 can be any of various catalysts known in the art. For example, in some implementations, the SCR catalyst 152 is a vanadium-based catalyst, and in other implementations, the SCR catalyst is a zeolite-based catalyst, such as a Cu-Zeolite or a Fe-Zeolite catalyst. In one representative embodiment, the reductant is aqueous urea and the SCR catalyst 152 is a zeolite-based catalyst.

The AMOX catalyst 160 can be any of various flow-through catalysts configured to react with ammonia to produce mainly nitrogen. Generally, the AMOX catalyst 160 is utilized to remove ammonia that has slipped through or exited the SCR catalyst 152 without reacting with NO_(x) in the exhaust. In certain instances, the system 10 can be operable with or without an AMOX catalyst. Further, although the AMOX catalyst 160 is shown as a separate unit from the SCR catalyst 152, in some implementations, the AMOX catalyst can be integrated with the SCR catalyst, e.g., the AMOX catalyst and the SCR catalyst can be located within the same housing.

The exhaust after-treatment system 100 includes various sensors, such as temperature sensors 124A-F, pressure sensor 126, oxygen sensor 162, NO_(x) sensors 164A-D, NH₃ sensors 166A-C, dual ammonia/NO_(x) sensors (not shown) and the like, that are disposed throughout the exhaust gas after-treatment system. The various sensors may be in electrical communication with the controller 130 to monitor operating conditions and control the engine system 10, including the exhaust after-treatment system 100. In the illustrated embodiment, the exhaust gas after-treatment system 100 includes NO_(x) sensor 164A upstream of the oxidation catalyst 140, NO_(x) sensor 164B embedded within the SCR catalyst 152, NO_(x) sensor 164C intermediate the SCR catalyst and AMOX catalyst 160, and NO_(x) sensor 164D downstream of the AMOX catalyst. Further, the illustrated exhaust gas after-treatment system 100 includes NH₃ sensor 166A upstream of the SCR catalyst 125, NH₃ sensor 166B embedded within the SCR catalyst 152, and NH₃ sensor 166C downstream of the AMOX catalyst 160.

Although the exhaust after-treatment system 100 shown includes one of an oxidation catalyst 140, particulate filter 142, SCR catalyst 152, and AMOX catalyst 160 positioned in specific locations relative to each other along the exhaust flow path, in other embodiments, the exhaust after-treatment system may include more than one of any of the various catalysts positioned in any of various positions relative to each other along the exhaust flow path as desired. Further, although the oxidation catalyst 140 and AMOX catalyst 160 are non-selective catalysts, in some embodiments, the oxidation and AMOX catalysts can be selective catalysts.

The controller 130 controls the operation of the engine system 10 and associated sub-systems, such as the engine 11 and exhaust gas after-treatment system 100. The controller 130 is depicted in FIG. 2 as a single physical unit, but can include two or more physically separated units or components in some embodiments if desired. Generally, the controller 130 receives multiple inputs, processes the inputs, and transmits multiple outputs. The multiple inputs may include sensed measurements from the sensors and various user inputs. The inputs are processed by the controller 130 using various algorithms, stored data, and other inputs to update the stored data and/or generate output values. The generated output values and/or commands are transmitted to other components of the controller and/or to one or more elements of the engine system 10 to control the system to achieve desired results, and more specifically, achieve desired exhaust gas emissions.

The controller 130 includes various modules for controlling the operation of the engine system 10. For example, the controller 130 includes one or more modules for controlling the operation of the particulate filter 142 as described above. The controller 130 also includes one or more modules for controlling the operation of the SCR system 150. The controller 130 further includes one or more modules for controlling the operation of the engine 11. Additionally, in the event the oxidation catalyst 140 and AMOX catalyst 160 are selectively controllable, the controller 130 can include one or more modules for controlling the operation of the respective oxidation and AMOX catalysts.

Referring to FIG. 3, and according to one embodiment, the controller 130 includes several modules for controlling operation of the SCR system 150 to provide efficient reduction of NO_(x) during transient and steady state operations, while reducing ammonia slip from the tailpipe. More specifically, the controller 130 includes a NO_(x) reduction target module 300, at least one ammonia target module (e.g., feedforward ammonia target module 310 and feedback ammonia target module 344) a reductant target module 330, an NH₃ storage module 350, an AMOX NH₃ conversion module 380, a reductant limiting module 390, and a corrected tailpipe NO_(x) module 397. Generally, the modules are independently and/or cooperatively operated to achieve optimal NO_(x) conversion efficiency on the SCR catalyst 152 while minimizing ammonia slip and urea consumption. The controller 130 is communicable in data receiving and/or transmitting communication with several sub-systems of the engine system 10, such as engine controls 167, PM filter system controls 168, and SCR system controls 169.

NO_(x) Reduction Target Module

Referring to FIG. 4, the NO_(x) reduction target module 300 is operable to determine a NO_(x) reduction requirement 304. The NO_(x) reduction requirement represents the amount of NO_(x) that should be reduced from the exhaust gas stream on the SCR catalyst 152 to achieve a predetermined exhaust gas emissions limit. In other words, the NO_(x) reduction target module 300 determines the NO_(x) reduction requirement 304 necessary to achieve the desired tailpipe NO_(x) level 306. The desired amount of NO_(x) at the tailpipe, e.g., desired tailpipe NO_(x) level 306 (see FIGS. 4 and 16), is representative of the amount of NO_(x) allowed to exit the tailpipe pursuant to regulated emissions standards.

Generally, the NO_(x) reduction requirement 304 is expressed as the fraction of the NO_(x) in the exhaust gas stream to be reduced. The NO_(x) reduction requirement can also be expressed in terms of a NO_(x) reduction rate or the rate at which NO_(x) should be reduced to achieve the predetermined exhaust gas emissions limit. In certain implementations, the NO_(x) reduction target module 300 is communicable in data receiving communication with the NO_(x) sensor 164A to determine the amount of NO_(x) present in the exhaust gas stream prior to entering the SCR catalyst 152. Alternatively, or additionally, in some implementations, the amount of NO_(x) present in the exhaust gas stream can be estimated via operation of an engine operating conditions module 302. The engine operating conditions module 302 compares the operating conditions of the engine 11 against a stored operating map containing predetermined exhaust NO_(x) levels for various operating conditions of the engine to determine an estimated amount of NO_(x) in the exhaust gas stream. The NO_(x) reduction target module 300 compares the actual or estimated amount of NO_(x) in the exhaust gas stream at the engine outlet to a desired level of NO_(x) 306 in the exhaust gas emitted from the tailpipe to determine the NO_(x) reduction requirement 304.

Ammonia Target Modules

The controller 130 includes an ammonia target module operable to determine an ammonia addition requirement. As defined herein, the ammonia addition requirement is the amount of ammonia that should be added to the exhaust gas stream to reduce the NO_(x) in the exhaust gas stream to the desired level for meeting the emissions standards. In certain embodiments, the controller 130 includes the feedforward ammonia target module 310 for determining an ammonia addition requirement 326 using a feedforward methodology (see FIG. 5A). In other embodiments, the controller 130 includes the feedback ammonia target module 344 for determining an ammonia addition requirement 348 using a feedback methodology (see FIG. 5B). In yet some embodiments, the controller 130 includes both the feedforward ammonia target module 310 and the feedback ammonia target module 344.

Referring first to FIG. 5A, the feedforward ammonia target module 310 receives as input the NO_(x) reduction requirement 304 from the NO_(x) reduction target module 311 (see FIG. 4), an NH₃ storage modifier 352 from the NH₃ storage module 350 (see FIG. 10), and a current SCR catalyst inlet NH₃ flow rate 335 from the reductant hydrolysis module 333 (see FIG. 7) and utilized by the module 310 to determine the ammonia addition requirement 326. In the representative illustrated embodiment, the feedforward ammonia target module 310 includes a NO_(x) reduction efficiency module 312, an SCR catalyst inlet NO₂/NO_(x) ratio module 314, an SCR catalyst inlet exhaust properties module 316, an SCR catalyst bed temperature module 318, an SCR catalyst inlet NO_(x) module 320, an SCR catalyst space velocity module 322, and a NO_(x) reduction reaction rate module 324.

The NO_(x) reduction efficiency module 312 is operable to determine the maximum efficiency of NO_(x) reduction on the SCR catalyst 152. Generally, the NO_(x) reduction efficiency module 312 considers a desired NO_(x) conversion efficiency and the condition of the SCR catalyst.

The desired NO_(x) conversion efficiency can be any of various efficiencies and be dependent on the difference between the amount of NO_(x) in the exhaust gas stream at the engine outlet with the desired amount of NO_(x) in the exhaust gas stream at the tailpipe outlet. For example, in some implementations, the desired NO_(x) conversion efficiency of the SCR catalyst 152 can be the efficiency necessary for achieving the desired tailpipe NO_(x) level 306 at the SCR catalyst outlet. However, in embodiments having an AMOX catalyst, the desired NO_(x) conversion efficiency of the SCR catalyst 152 can be lower than if no AMOX catalyst is being used because the AMOX catalyst can reduce ammonia slipping from the SCR catalyst.

The condition of the SCR catalyst 152 affects the efficiency of the SCR catalyst. The more degraded the condition of the SCR catalyst, the lower the maximum efficiency of NO_(x) reduction on the SCR catalyst 152. Accordingly, the NO_(x) reduction efficiency module 312 is operable to compare the desired NO_(x) conversion efficiency with the maximum NO_(x) conversion efficiency of the SCR catalyst 152 and output the smaller of the two efficiencies to the feedforward ammonia target module 310. The feedforward ammonia target module 310 then utilizes the smaller of the desired and maximum NO_(x) conversion efficiencies determined by the NO_(x) reduction efficiency module 312 to determine the ammonia addition requirement 326. Generally, the lower the smaller NOx conversion efficiency, the lower the ammonia addition requirement 326.

The NO_(x) reduction efficiency module 312 can determine the maximum NO_(x) conversion efficiency of the SCR catalyst 152 in various ways, such as described in pending U.S. Provisional Patent Application No. 61/120,297, filed Dec. 5, 2008, which is incorporated herein by reference. Moreover, the condition of the SCR catalyst 152 can be indicated by an SCR catalyst degradation factor as described herein. The SCR catalyst degradation factor can be determined by an SCR catalyst degradation factor module, such as module 368 described below in relation to FIG. 11.

The SCR catalyst inlet NO₂/NO_(x) ratio module 314 is operable to predict the NO₂/NO_(x) ratio of the exhaust gas in the exhaust gas stream at the inlet of the SCR catalyst 152. In some implementations, the NO₂/NO_(x) ratio is expressed as the following ratio:

$\begin{matrix} \frac{{NO}_{2}}{{NO} + {NO}_{2}} & (1) \end{matrix}$ where NO is the mass concentration of nitrogen monoxide in a predetermined volume of exhaust gas and NO₂ is the mass concentration of nitrogen dioxide in the predetermined volume of exhaust gas.

The SCR catalyst inlet exhaust properties module 316 is operable to determine various properties of the exhaust gas at the inlet of the SCR catalyst 152. The properties can include, for example, the mass flow rate of the exhaust and the temperature of the exhaust. In some implementations, the exhaust gas properties are predicted based on predetermined exhaust property values for predetermined operating conditions of the engine system 10. For example, the SCR catalyst inlet exhaust properties module 316 can include an exhaust properties map, table or vector comparing predetermined exhaust property values with engine system operating conditions, such as the operating load and/or speed of the engine 11. In certain implementations, the SCR catalyst inlet exhaust properties module 316 determines the exhaust gas properties by processing input from any of various sensors known in the art, such as mass flow and temperatures sensors.

The SCR catalyst bed temperature module 318 is operable to determine the bed temperature of the SCR catalyst 152. The bed temperature of the SCR catalyst 152 can be determined based on one or more temperature sensors embedded in the SCR catalyst, such as temperature sensor 124D, or predicted by a module (see, e.g., AMOX catalyst bed temperature module 386 of FIG. 14) that uses various operating parameters of the system, such as the exhaust gas mass flow rate and temperature before and after the SCR catalyst 152. Accordingly, although the illustrated embodiments use an SCR catalyst bed temperature sensor 124D for determining the temperature of the SCR catalyst bed, in other embodiments, the sensor is replaced or supplemented with an SCR catalyst bed temperature module operable to predict or estimate the temperature of the SCR catalyst bed.

The SCR catalyst inlet NO_(x) module 320 is operable to determine the concentration of NO_(x) in the exhaust gas at the inlet of the SCR catalyst 152. The NO_(x) concentration can be predicted based on predetermined exhaust conditions corresponding to predetermined operating conditions of the engine system 10. For example, the module 320 can access an exhaust properties map, table or vector such as described above to estimate the NO_(x) concentration in the exhaust. Alternatively, or additionally, the concentration of NO_(x) in the exhaust gas upon entering the SCR catalyst 152 can be measured using the first NO_(x) sensor 164A positioned upstream of the SCR catalyst.

The SCR catalyst space velocity module 322 is operable to determine the space velocity of the SCR catalyst 152. Generally, the space velocity of the SCR catalyst 152 represents the amount of NO_(x) in the exhaust gas stream that is reactable within the SCR catalyst over a given time. Accordingly, the space velocity of the SCR catalyst 152 typically is represented in terms of per unit time, e.g., 1/hour, 1,000/hour, etc. The space velocity of the SCR catalyst 152 is based on various exhaust gas and catalyst conditions. For example, the space velocity can be based at least partially on the volume and/or reaction, or bed, surface area of the SCR catalyst, and the density, viscosity and/or flow rate of the exhaust gas. In some implementations, the SCR catalyst space velocity module 322 determines the space velocity of the SCR catalyst 152 by receiving inputs concerning operating conditions of the engine system 10, and, based on the operation conditions, obtaining the space velocity of the SCR for the given conditions by accessing a table or map stored on the module. The table can include various predetermined space velocities obtained via experimental testing and calibration for a given SCR catalyst operating under the various operating conditions achievable by the engine system 10.

The NO_(x) reduction reaction rate module 324 is operable to predict the rate at which ammonia reacts with and reduces NO_(x) on the SCR catalyst 152. The predicted NO_(x) reaction rate is at least partially dependent on the NO_(x) composition or concentration of the exhaust gas and the frequency of the various types of NO_(x) reduction reactions occurring on the SCR catalyst 152. Generally, NO_(x) is reduced by ammonia in one of the following three most active stoichiometric chemical reactions:

$\begin{matrix} \left. {{NH}_{3} + {\frac{1}{2}{NO}} + {\frac{1}{2}{NO}_{2}}}\rightarrow{N_{2} + {\frac{3}{2}H_{2}O}} \right. & (2) \\ \left. {{NH}_{3} + {NO} + {\frac{1}{4}O_{2}}}\rightarrow{N_{2} + {\frac{3}{2}H_{2}O}} \right. & (3) \\ \left. {{NH}_{3} + {\frac{3}{4}{NO}_{2}}}\rightarrow{{\frac{7}{8}N_{2}} + {\frac{3}{2}H_{2}O}} \right. & (4) \end{matrix}$

The predicted NO_(x) reaction rate is also at least partially dependent on the ammonia concentration rate, the bed temperature of the SCR catalyst 152, and the space velocity of the SCR catalyst. Further, in some implementations, the predicted NO_(x) reaction rate is also at least partially dependent on the degradation factor or condition of the SCR catalyst 152. The predicted NO_(x) reaction rate can be expressed as the sum of a predicted NO_(x) reaction rate for reducing NO according to Equations 2 and 3 above and a predicted NO_(x) reaction rate for reducing NO₂ according to Equations 3 and 4 above.

Based at least partially on the desired NO_(x) conversion efficiency, the NO₂/NO_(x) ratio of the exhaust gas, the exhaust flow rate, the temperature and condition of the SCR catalyst 152 bed, the amount of NO_(x) and NH₃ at the inlet of the SCR catalyst, and the NO_(x) reduction reaction rate, the ammonia target module determines the ammonia addition requirement 326. In some embodiments, the ammonia addition requirement 326 is also at least partially based on an NH₃ storage modifier 352 determined by an NH₃ storage module 350 as will be described in more detail below (see FIG. 7).

According to another embodiment shown in FIG. 5B, the ammonia addition requirement, e.g., ammonia addition requirement 348, can be determined by the feedback ammonia target module 344. The feedback ammonia target module 344 receives as input the desired tailpipe NO_(x) level 306, the amount of NH₃ exiting the tailpipe as sensed by the tailpipe NH₃ sensor 166C, the NH₃ storage modifier 352, and a corrected tailpipe NO_(x) value 399 (see FIG. 17). Further, the feedback ammonia target module 344 includes an exhaust flow properties module 345 and a tailpipe NO_(x) feedback module 347. In contrast to the feedforward ammonia target module 310, the feedback ammonia target module 344 relies mainly on the properties of the exhaust gas stream after passing through the SCR catalyst 152 and adjusts the reductant dosing rate to compensate for errors and inconsistencies in the SCR system 150.

The exhaust flow properties module 345 is operable to determine various conditions of the exhaust gas stream, e.g., temperature, flow rate, etc., in a manner similar to that described above in relation to SCR catalyst inlet exhaust properties module 316.

The tailpipe NO_(x) feedback module 347 is operable to determine a tailpipe NO_(x) feedback value that can be utilized by the feedback ammonia target module 344 for determining the ammonia addition requirement 348. The tailpipe NO_(x) feedback value accounts for inconsistencies in the SCR system 150, such as modeling errors, catalyst aging, sensor aging, reductant concentration variations, reductant injector delays, which can reduce the efficiency of the system. Therefore, the tailpipe NO_(x) feedback module 396 is operable to modulate the tailpipe NO_(x) feedback value to increase the efficiency of the SCR system 150 and achieve the desired NO_(x) conversion efficiency despite inconsistencies that may be present in the system.

The tailpipe NO_(x) feedback module 347 generates the tailpipe NO_(x) feedback value by comparing the sensed amount of NO_(x) as detected by the tailpipe NO_(x) sensor 164D with the desired or targeted tailpipe NO_(x) amount 306. Accordingly, the tailpipe NO_(x) feedback value is at least partially dependent on the difference between the sensed tailpipe NO_(x) and the targeted or desired tailpipe NO_(x) 306. Generally, the greater the difference between the sensed tailpipe NO_(x) and the targeted tailpipe NO_(x) 306, the higher the ammonia addition requirement 348. For example, if the sensed amount of tailpipe NO_(x) is relatively high compared to the targeted tailpipe NO_(x) 306, then the feedback ammonia target module 344 can increase the ammonia addition requirement 348. As will be explained in more detail below, an increase in the ammonia addition requirement 348 can result in more reductant being added to the exhaust gas stream for increased NO_(x) conversion on the SCR catalyst 152. Conversely, if the sensed amount of tailpipe NO_(x) is relatively low compared to the targeted tailpipe NO_(x) 306, then the feedback ammonia target module 344 can decrease the ammonia addition requirement, which may consequently result in less reductant being added to the exhaust gas stream to conserve reductant, and thus increase the efficiency of the SCR system 150.

In certain embodiments, because of the cross-sensitivity of some NO_(x) sensors to ammonia, the feedback ammonia target module 344 is utilized by the SCR system 150 to generate the ammonia addition requirement only when ammonia is not slipping from the SCR system 150, e.g., slipping out of the tailpipe. Whether ammonia is slipping from the tailpipe can be sensed by the tailpipe NH₃ sensor 166C and/or predicted by the AMOX NH₃ conversion module 380, as will be described in more detail below.

In certain embodiments, the controller 130 includes a control logic selection algorithm (not shown) configured to select one of the ammonia addition requirements 326, 348 to act as the ammonia addition requirement for the SCR system 150 based at least partially on whether NH₃ is slipping from the tailpipe. In other words, the module used for determining the ammonia addition requirement for the SCR system 150 is switchable based on whether the SCR system is operating in a tailpipe NH₃ slip mode or a tailpipe NH₃ non-slip mode. More specifically, when NH₃ is slipping from the tailpipe, the ammonia addition requirement 326 determined by the feedforward ammonia target module 310 is communicated to the reductant target module 330 and used in the determination of the reductant injection requirement 332 (see FIG. 8). Conversely, when NH₃ is not slipping from the tailpipe, the ammonia addition requirement 348 determined by the feedback ammonia target module 344 is communicated to the reductant target module 330 and used in the determination of the reductant injection requirement 332. In some implementations, the control logic selection algorithm of the controller 130 determines the ammonia addition requirement based on a combination, e.g., an average, of the ammonia addition requirements 326, 348 regardless of whether ammonia is slipping from the tailpipe. In certain implementations, the ammonia addition requirement 326 can be adjusted according to the ammonia addition requirement 348.

In some embodiments, the feedback ammonia target module 344 includes a signal correction algorithm (not shown) configured to filter the signal from the tailpipe NO_(x) sensor 164D such that the signal is suitable for yielding a more accurate NO_(x) concentration at the tailpipe when ammonia is slipping from the tailpipe. Accordingly, in some implementations, the ammonia addition requirement 348 generated by the feedback ammonia target module 344 can be communicated to the reductant target module 330 during operation in the tailpipe NH₃ slip or non-slip mode.

As described above, the controller 130 can utilize the feedforward ammonia target module 310, the feedback ammonia target module 344, or both to determine an ammonia addition requirement for the SCR system 150. Once determined, the ammonia addition requirement, e.g., ammonia addition requirement 326, ammonia addition requirement 348, or combination of both, is communicated to the reductant target module 330, or more specifically, the inverse reductant hydrolysis module 334 of the reductant target module. As used hereafter, the ammonia addition requirement communicated to the reductant target module 330 will be referenced as the ammonia addition requirement 326. Nevertheless, it is recognized that any reference to the ammonia addition requirement 326 can be substituted with the ammonia addition requirement 348 or a combination of the ammonia addition requirements 326, 348.

Reductant Target Module

Referring to FIG. 6, the reductant target module 330 includes a reductant hydrolysis module 333 and an inverse reductant hydrolysis module 334. As will be described in more detail below, the reductant hydrolysis module 333 is operable to determine a current SCR catalyst inlet NH₃ flow rate 335 and a current SCR catalyst inlet HNCO flow rate 336 based on the current reductant dosing rate (see FIG. 7). The current SCR catalyst inlet NH₃ flow rate 335 and current SCR catalyst inlet HNCO flow rate 336 are then communicated to other various modules of the control system 150. In contrast to the reductant hydrolysis module 333, the inverse reductant hydrolysis module 334 is operable to receive the ammonia addition requirement 326 from the ammonia target module 310 and determine a reductant injection requirement or dosing rate 332, i.e., the amount of reductant necessary to achieve the ammonia addition requirement 326 (see FIG. 8). Based on the reductant injection requirement 332, the controller 130 commands the SCR system controls to inject an amount of reductant corresponding to the reductant injection requirement 332.

The reductant can be any of various reductants known in the art. For example, in one implementation, the reductant is ammonia. In other implementations, the reductant is urea, which breaks down into ammonia and other components as will be described in more detail below.

Reductant Hydrolysis Module

Referring back to FIG. 7, the reductant hydrolysis module 333 includes an NH₃ conversion efficiency table 337, an isocyanic acid (HNCO) conversion efficiency table 338, and an SCR catalyst inlet exhaust properties module 339. The SCR catalyst inlet exhaust properties module 339 is operable to determine the mass flow rate of the exhaust gas stream in a manner similar to that described above in relation to SCR catalyst inlet exhaust properties module 316 of FIG. 5. The reductant hydrolysis module 333 is communicable in data receiving communication with the reductant delivery mechanism 190 for receiving a current reductant dosing rate 383 and the exhaust temperature sensor 124B for receiving the temperature of the exhaust.

As described above, in implementations where the reductant is urea, the reductant hydrolysis module 333 is operable to determine the amount of ammonia and isocyanic acid entering the SCR catalyst 152. According to one embodiment, the reductant hydrolysis module 333 is operable to follow the schematic flow chart 400 of FIG. 9 to determine the current SCR catalyst inlet NH₃ and HNCO flow rates 335, 336, respectively. The exhaust temperature is sensed, such as by the temperature sensor 124B, or estimated, at 410 and the exhaust mass flow rate is estimated by the SCR catalyst inlet exhaust properties module 339 at 420. Based at least partially on the exhaust temperature determined at 410 and the exhaust mass flow rate determined at 420, the conversion efficiency of urea to NH₃ is determined at 430 and the conversion efficiency of urea to isocyanic acid (HNCO) is determined at 440. Accordingly, the conversion efficiencies of urea to NH₃ and isocyanic acid are a function of the exhaust gas temperature and mass flow rate. The NH₃ and HNCO conversion efficiencies are determined by comparing the exhaust gas temperature and mass flow rate to one or more predetermined efficiency values listed on NH₃ and HNCO conversion efficiency look-up tables 337, 338, respectively.

According to the reductant injection requirement 332 received by the SCR inlet ammonia and isocyanic acid module 360 from the reductant target module 330, urea is injected into the exhaust gas stream by a urea injector at 450. The urea is mixed with the exhaust gas stream flowing through an exhaust pipe between the urea injector and the surface of SCR catalyst 152. As the urea flows along the exhaust pipe, it reacts with the exhaust gas to form NH₃ at 460 and HNCO at 470. The NH₃ and HNCO in the exhaust gas stream then enter the SCR catalyst 152 as the current SCR catalyst inlet NH₃ flow rate 335 and current SCR catalyst inlet HNCO flow rate 336, respectively. After the HNCO enters the SCR catalyst 152, the catalyst bed promotes a reaction between at least a portion of the HNCO and water (H₂O) in the exhaust gas stream to form additional NH₃ at 480. The current SCR catalyst inlet NH₃ flow rate 335 and the current HNCO to NH₃ flow rate 341, i.e., the NH₃ from the conversion of HNCO to NH₃ occurring within the SCR catalyst 152 at 480, are combined to provide an estimation of the total amount of ammonia within the SCR catalyst, e.g., the current SCR catalyst NH₃ flow rate 343. The estimated amount of HNCO that is not converted to NH₃ at 480 flows through and out of the SCR catalyst 152 at an SCR catalyst outlet HNCO flow rate 349.

As discussed above, the amount of urea converted to NH₃ is at least partially dependent on the NH₃ conversion efficiency. In an ideal situation, the NH₃ conversion efficiency is 100% such that the all the urea converts to 2-parts ammonia and 1-part carbon dioxide without any intermediate conversion to HNCO according to the following equation: NH₂—CO—NH₂(aq)+H₂O→2NH₃(g)+CO₂  (5)

In actuality, the NH₃ conversion efficiency is typically less than 100% such that the urea converts to ammonia and isocyanic acid according to the following equation: NH₂—CO—NH₂(s)→NH₃(g)+HNCO(g)  (6)

The remaining isocyanic acid converts to ammonia and carbon dioxide CO₂ according to the HNCO conversion efficiency. In ideal situations, the HNCO conversion efficiency is 100% such that all the isocyanic acid converts to 1-part ammonia and 1-part carbon dioxide within the SCR catalyst 152 according to the following equation: HNCO(g)+H₂O(g)→NH₃(g)+CO₂(g)  (7)

Typically, however, the HNCO conversion efficiency is less than 100% such that some of the HNCO is converted to ammonia and carbon dioxide and the remaining portion of HNCO is unconverted within the SCR catalyst 152. The flow rate of NH₃ into the SCR catalyst 152 ({dot over (n)}_(NH) ₃ (s)) per flow rate of injected urea ({dot over (n)}_(urea)(s)) is estimated according to the following equation:

$\begin{matrix} {\frac{{\overset{.}{n}}_{{NH}_{3}}(s)}{{\overset{.}{n}}_{urea}(s)} = {\frac{1}{{\tau\; s} + 1}\left( {1 - {\mathbb{e}}^{{- x}/L}} \right){\eta_{{NH}_{3}}\left( {\overset{.}{m},T} \right)}}} & (8) \end{matrix}$ where τ is the mixing time constant, s is a complex variable used for Laplace transforms, L is the characteristic mixing length, x is the distance from the urea injector to the SCR catalyst inlet or face, and η_(NH) ₃ is the NH₃ conversion efficiency from urea, which is based on the mass flow rate ({dot over (m)}) and temperature (T) of the exhaust gas. The complex variable s can be expressed as σ+jω, where σ represents the amplitude and ω represents the frequency of a sinusoidal wave associated with a given urea dosing rate input. The mixing time constant is predetermined based at least partially on the Federal Test Procedure (FTP) heavy-duty transient cycle for emission testing of heavy-duty on-road engines. Assuming 100% conversion efficiency, the mixing time constant is tuned with the FTP data to eliminate transient mismatches. The characteristic length L is defined as the major linear dimension of the exhaust pipe that is substantially perpendicular to the exhaust gas flow. For example, for a cylindrical exhaust pipe, the major linear dimension is the diameter of the pipe. In some embodiments, the distance from the urea injector to the SCR catalyst face x is between about 5 and 15 times the characteristic length. In specific implementations, the distance x is about 10 times the characteristic length.

Similarly, the flow rate of isocyanic acid (HNCO) into the SCR catalyst 152 ({dot over (n)}_(HNCO)(s)) per flow rate of injected urea ({dot over (n)}_(urea)(s)) is estimated according to the following equation:

$\begin{matrix} {\frac{{\overset{.}{n}}_{HNCO}(s)}{{\overset{.}{n}}_{urea}(s)} = {\frac{1}{{\tau\; s} + 1}\left( {1 - {\mathbb{e}}^{{- x}/L}} \right){\eta_{HNCO}\left( {\overset{.}{m},T} \right)}}} & (9) \end{matrix}$ where η_(HNCO) is the HNCO conversion efficiency from urea. The conversion efficiencies of urea to ammonia (η_(NH) ₃ ) and urea to isocyanic acid (η_(HNCO)) is predetermined based on operating parameters of the engine system 10. In some implementations, the conversion efficiencies are tuned by comparing a measurement of the NH₃ and HNCO at the inlet of the SCR catalyst 152 with the expected amount of NH₃ and HNCO based on the stoichiometric reaction of Equation 6 while dosing urea into exhaust at specific mass flow rates and temperatures. Inverse Reductant Hydrolysis Module

Referring now to FIG. 8, based at least partially on the ammonia addition requirement 326 received from the ammonia target module 310, the inverse reductant hydrolysis module 334 of the reductant target module 330 is operable to determine the reductant injection requirement 332 to achieve the ammonia addition requirement 326 generated by the ammonia target module 310. In some implementations, the process used by the inverse reductant hydrolysis module 334 to determine the reductant injection requirement 332 is similar to the process illustrated in flow chart 400, but inverted. In other words, the same techniques used in flow chart 400 to determine the current SCR catalyst inlet NH₃ flow rate 335 can be used to determine the reductant injection requirement 332, but in a different order.

For example, in the flow chart 400, the actual urea dosing rate is known and used to determine the flow of NH₃ into the SCR catalyst 152. In contrast, in the process used by the inverse reductant hydrolysis module 334, the ammonia addition requirement 326, e.g., the desired or estimated flow of NH₃ into the SCR catalyst 152, is known and used to determine the corresponding reductant injection requirement, e.g., dosing rate, necessary to achieve the desired NH₃ flow rate. The reductant injection requirement 332 is determined by predicting the hydrolysis rates and conversion efficiencies of urea to NH₃ and HNCO based on the temperature and mass flow rate of the exhaust gas stream. For example, the inverse reductant hydrolysis module 334 can include an NH₃ conversion efficiency table, HNCO conversion efficiency table, and an SCR catalyst inlet exhaust properties module similar to the reductant hydrolysis module 333. Alternatively, the inverse reductant hydrolysis module 334 can access the NH₃ conversion efficiency table 337, HNCO conversion efficiency table 338, and output of the SCR catalyst inlet exhaust properties module 339 of the reductant hydrolysis module 333.

In some implementations, with the desired flow rate of NH₃ into the SCR catalyst 152 ({dot over (η)}_(NH) ₃ (s)), e.g., the ammonia addition requirement, known, the reductant injection requirement 332 is determined from Equation 8 above by solving for the flow rate of injected urea {dot over (η)}_(urea)(s). In one specific implementation, the reduction injection requirement 332 expressed in terms of mL/hr of urea is approximately equal to:

$\begin{matrix} {{\frac{mL}{hr}{Urea}} \approx {1.85 \star {f(a)} \star {\overset{.}{m}{NO}_{x}}}} & (10) \end{matrix}$ where {dot over (m)}NO_(x) is equal to the mass flow rate of the total amount of NO_(x) in the exhaust gas stream expressed in terms of grams/hour and f(a) is a non-dimensional piecewise function where a is equal to the NO₂/NO_(x) ratio expressed above in Equation 1. When NO is greater than or equal to NO₂, i.e., NO₂/NO_(x)≦0.5, f(a) is equal to about one, and when NO is less than or equal to NO₂, i.e., NO₂/NO_(x)≧0.5 f(a) is equal to:

$\begin{matrix} \frac{2\left( {a + 1} \right)}{3} & (11) \end{matrix}$

In another specific embodiment, the reduction injection requirement 332 is determined based on the ideal stoichiometric conversion of urea to ammonia and the ideal stoichiometric reduction of NO_(x) on the SCR catalyst 152. When the level of NO in the exhaust gas stream is greater than or equal to the level of NO₂ in the exhaust gas, the amount of urea for reducing one gram of NO_(x) is represented by Equation 12 below. When the level of NO in the exhaust gas is less than or equal to the level of NO₂ in the exhaust gas, the amount of urea for reducing one gram of NO_(x) is represented by Equation 13 below, where a is equal to the NO₂/NO_(x) ratio expressed above in Equation 1. As used in Equations 12 and 13, MW_(Urea) is the molecular weight of the urea to be injected and MW_(NOx) is the molecular weight of NO_(x) in the exhaust gas stream.

$\begin{matrix} {0.5 \star \left( \frac{M\; W_{Urea}}{M\; W_{NOx}} \right)} & (12) \\ {0.5 \star \left( \frac{M\; W_{Urea}}{M\; W_{{NO}\; x}} \right) \star \frac{2\left( {a + 1} \right)}{3}} & (13) \end{matrix}$

Based on Equations 12 and 13, the flow rate of urea in terms of grams per second can be expressed in terms of the mass flow rate of NO_(x) ({dot over (m)}_(NOx)) in the exhaust gas stream. For example, when the amount of NO in the exhaust gas stream is more than or equal to the amount of NO₂ in the exhaust gas stream, the flow rate of urea can be expressed according to the following equation:

$\begin{matrix} \frac{{\overset{.}{m}}_{NOx}}{0.5 \star \left( \frac{M\; W_{Urea}}{M\; W_{{NO}\; x}} \right)} & (14) \end{matrix}$ where MW_(Urea) is the molecular weight of urea, and MW_(NOx) is the molecular weight of NO_(x) in the exhaust gas stream. When the amount of NO in the exhaust gas stream is less than or equal to the amount of NO₂ in the exhaust gas stream, the flow rate of urea can be expressed according to the following equation:

$\begin{matrix} \frac{{\overset{.}{m}}_{{NO}\; x}}{0.5 \star {\left( \frac{M\; W_{Urea}}{M\; W_{{NO}\; x}} \right)\frac{2\left( {a + 1} \right)}{3}}} & (15) \end{matrix}$

In some implementations, the inverse reductant hydrolysis module 334 is communicable in data receiving communication with the reductant modifier module 390 to receive a reductant modifier requirement 342 (see FIG. 16). As will be described in more detail below, the reductant modifier requirement 342 includes instructions for increasing or decreasing the reductant injection requirement 332 based on whether one or more reductant limiting conditions are present. Accordingly, the inverse reductant hydrolysis module 334 is operable to modify the reductant injection requirement 332 according to the reductant modifier requirement 342.

Ammonia Storage Module

Referring to FIG. 10, the NH₃ storage module 350 is operable to determine an ammonia storage modifier or storage compensation command 352. Generally, the ammonia storage modifier 352 includes information regarding the state of ammonia storage on the SCR catalyst 152. More specifically, the ammonia storage modifier 352 includes instructions on whether ammonia entering the SCR catalyst 152 should be increased or decreased, e.g., whether the ammonia addition requirement should be increased or decreased. The ammonia target module 310 is communicable in data receiving communication with the NH₃ storage module 350 to receive the ammonia storage modifier 352 as an input value. Based on the ammonia storage modifier 352, the ammonia target module 310 is operable to adjust, e.g., increase or decrease, the ammonia addition requirement 326 to compensate for modulations in the ammonia storage level on the SCR catalyst 152 and maintain a sufficient amount of stored NH₃ on the SCR catalyst for transient operations of the engine 11.

As discussed above, the performance of the SCR system 150 is defined by the conversion efficiency of NO_(x) in the exhaust gas stream and the amount of ammonia that has slipped out of the tail-pipe over both steady-state and transient duty cycles. During transient duty cycles, the response of conventional control systems that monitor only the NO_(x) level at the tailpipe outlet typically are limited by the dynamics of the reductant dosing system, the cross-sensitivity of the NO_(x) sensor to NH₃, and other factors. Accordingly, conventional control systems may have unstable feedback controls during transient duty cycles. To improve the response and feedback controls during transient duty cycles, the SCR system 150 utilizes NH₃ stored on the SCR catalyst to manage transient NO_(x) spikes that may occur during transient operation or cycles of the engine 11. Further, NH₃ stored on the SCR catalyst 152 can be used to reduce NO_(x) when engine system operating conditions, such as low SCR catalyst bed temperatures, require a reduction or elimination of reductant dosing. The NH₃ storage module 350 is configured to monitor and regulate the amount of ammonia stored on the SCR catalyst 152 such that a sufficient amount of stored NH₃ is maintained on the SCR catalyst to accommodate transient NO_(x) variations and low catalyst bed temperatures as well as reduce NH₃ slip.

The NH₃ storage module 350 includes a current NH₃ storage level module 354 and a target NH₃ storage level module 356. The modules 354, 356 process one or more inputs received by the NH₃ storage module 350 as will be explained in more detail below.

Current Ammonia Storage Level Module

Referring to FIG. 11, the current NH₃ storage level module 354 is communicable in data receiving communication with several sensors for receiving data sensed by the sensors. In the illustrated embodiment, the several sensors include at least the SCR catalyst bed temperature sensor 124C, NH₃ sensors 166A-C, and NO_(x) sensors 164A-D. The current NH₃ storage level module 354 also is capable of receiving an AMOX NH₃ conversion capability 382 value and a corrected tailpipe NO_(x) value 399 as will be described in further detail below.

The current NH₃ storage level module 354 also includes an SCR catalyst inlet exhaust properties module 358, an NH₃ flux module 364, an SCR catalyst inlet NO₂/NO_(x) ratio module 366, an SCR catalyst degradation factor module 368, an SCR catalyst NH₃ slip module 369, and an NH₃ desorption module 375. Based on input received from the sensors 124C, 166A,-C, 164A-D, the AMOX NH₃ conversion capability 382 (if an AMOX catalyst is used), the tailpipe NO_(x) feedback value 399, and operation of the modules 358, 364, 366, 368, 369, 375, the current NH₃ storage level module 354 is operable to determine the current NH₃ storage level 370 (e.g., an estimate of the current amount of NH₃ stored on the SCR catalyst 152 based at least partially on the SCR catalyst bed temperature), the current NH₃ slip 372 (e.g., an estimate of the current amount of NH₃ exiting the SCR catalyst), and the NH₃ maximum storage capacity 374 (e.g., an estimate of the maximum amount of NH₃ capable of being stored on the SCR catalyst based under current conditions). The fraction of the available storage on the SCR catalyst that is filled can be determined by dividing the current NH₃ storage level 370 by the NH₃ maximum storage capacity 374. The NO_(x) sensor 164B being embedded within the SCR catalyst 152 provides several advantages over prior art systems. For example, placing the NO_(x) sensor 164B inside the SCR catalyst 152 improves the monitoring of stored ammonia on the catalyst by reducing the signal-to-noise ratio of the NO_(x) sensor. The NO_(x) sensor 164B can be used with other NO_(x) sensors in the exhaust aftertreatment system 100 to quantify the spatial distribution of stored ammonia.

The SCR catalyst inlet exhaust properties module 358 is similar to SCR catalyst inlet exhaust properties module 316 of the ammonia target module 310. For example, the exhaust properties module 358 is operable to determine various properties of the exhaust, such as the temperature and flow rate of the exhaust.

The NH₃ flux module 364 is operable to determine the rate at which NH₃ flows into the SCR catalyst 152. The NH₃ flux module 364 can also process data concerning the amount of NH₃ present at the tailpipe outlet as sensed by the NH₃ sensor 166C. The NH₃ sensor 166C at the tailpipe outlet assists in the measurement and control of the tailpipe NH₃ slip by providing information regarding the tailpipe NH₃ slip to various modules of the controller 130. In some instances, the modules, e.g., the target NH₃ storage level module 356 and the reductant modifier module 390, adjust the urea dosing rate and the ammonia storage targets based at least partially on the tailpipe NH₃ slip information received from the NH₃ sensor.

The SCR catalyst inlet NO₂/NO_(x) ratio module 366 is similar to the SCR catalyst inlet NO₂/NO_(x) ratio module 314 of the ammonia target module 310. For example, the SCR catalyst inlet NO₂/NO_(x) ratio module 366 is operable to predict the NO₂/NO_(x) ratio of the exhaust gas in the exhaust gas stream according to Equation 1.

The SCR catalyst degradation factor module 368 is operable to determine a degradation factor representing the condition of the SCR catalyst 152. In certain implementations, the degradation factor indicates the amount the SCR catalyst 152 has degraded over time in comparison to the SCR catalyst when fresh or new. Therefore, the SCR degradation factor can be expressed as a percentage of new, a ratio of the current SCR catalyst condition to the condition of a new SCR catalyst, a ratio of the NO_(x) conversion efficiency of a degraded SCR catalyst to the NO_(x) conversion efficiency of a fresh SCR catalyst at a given standard operating condition of the engine system, a ratio of the NH₃ storage capacity of a degraded SCR catalyst to the NH₃ storage capacity of a fresh SCR catalyst at a given standard operating condition of the engine system, or a normalized value between zero and one with one being zero degradation and zero being a completely degraded catalyst.

Referring to FIG. 12, in one representative embodiment, the SCR catalyst degradation factor module 368 is operable to determine at least one of a first SCR catalyst degradation factor 762, a second SCR catalyst degradation factor 766, a storage capacity SCR catalyst degradation factor 700, and an NO_(x) conversion efficiency SCR catalyst degradation factor 710. One or more of the SCR catalyst degradation factors 700, 710, 762, 766 can be communicated to other components of the engine system 10, such as various modules of the controller 130, to facilitate accurate control of the urea reductant injection system and ensure proper operation of the SCR NO_(x) aftertreatment system to meet emission regulations. In certain implementations, two or more of the degradation factors 700, 710, 762, 766 can be compared or averaged to obtain a more accurate indication of the degradation of the SCR catalyst 152.

The SCR catalyst degradation factor module 368 includes a model-based approach module 760 that utilizes a model-based approach, which is based on physics based model of the SCR catalyst system, to determine the first SCR catalyst degradation factor 762. In one embodiment, the model-based approach module 760 determines the first SCR catalyst degradation factor 762 based at least partially on a plurality of inputs. Referring to FIG. 12, the plurality of inputs includes an SCR catalyst inlet exhaust gas temperature 740, an SCR catalyst inlet exhaust gas space velocity 742, an SCR catalyst bed temperature 744, an SCR catalyst inlet NO_(x) 746, an SCR catalyst inlet NO₂/NO_(x) ratio 748, regeneration information 750, the SCR catalyst outlet exhaust gas temperature 752, the SCR catalyst inlet NH₃ 335, the SCR catalyst inlet isocyanic acid 336, and the corrected tailpipe NO_(x) 399.

The SCR catalyst inlet exhaust gas temperature 740, SCR catalyst inlet exhaust gas space velocity 742, SCR catalyst bed temperature 744, SCR catalyst inlet NO_(x) 746, and SCR catalyst inlet NO₂/NO_(x) ratio 748 can be determined by and obtained from the SCR inlet exhaust properties module 316, catalyst space velocity module 322, SCR catalyst bed temperature module 318, SCR catalyst inlet NO_(x) module 320, and SCR catalyst inlet NO₂/NO_(x) ratio module 314, respectively, of the feedforward ammonia target module 310 (see FIG. 5A). As discussed above, the SCR catalyst inlet NH₃ 335 and SCR catalyst inlet isocyanic acid 336 are determined by the reductant hydrolysis module 333 (see FIG. 7). As will be discussed in more detail below, the corrected tailpipe NO_(x) 399 is determined by the corrected tailpipe NO_(x) module 397 (see FIG. 17). Although utilizing a corrected tailpipe NO_(x) 399 is desirable for heightened accuracy, in certain embodiments, the amount of NO_(x) exiting the SCR catalyst 152 as sensed by the NO_(x) sensor 164C can be used. The SCR catalyst outlet exhaust gas temperature 752 can be interpreted from a signal generated by the temperature sensor 124E positioned at the outlet of the SCR catalyst or intermediate the SCR catalyst and AMOX catalyst 160.

The regeneration information 750 includes any of various data regarding the performance and operating parameters of regeneration events on the SCR catalyst 152. The SCR catalyst 152 can be nominally regenerated to remove hydrocarbon and sulfur byproducts from the surface of the SCR catalyst. Generally, an SCR catalyst regeneration manager or controller (not shown) initiates and controls a regeneration of the SCR catalyst by increasing the temperature of catalyst bed to a threshold temperature appropriate for oxidizing and removing the hydrocarbons and sulfur byproducts caked on the surface of the SCR catalyst. The temperature of the catalyst bed can be increased via operation of the engine 11 and/or oxidation catalyst 140 using any of various techniques known in the art. As the SCR catalyst 152 is regenerated to remove hydrocarbon and sulfur by-products from the surface of the SCR catalyst, the SCR catalyst regeneration manager records at least some data concerning the nominal regeneration event. The regeneration information 750 includes at least some of the data recorded by the regeneration manager. In some embodiments, the regeneration information 750 includes the duration of regeneration events, the temperature of the SCR catalyst bed during regeneration events, and any other desirable information.

The regeneration information 750 can also include information regarding thermal regeneration of the PM filter 142, such as, for example, the duration of PM filter regeneration events, PM filter outlet properties, and the temperature gradients at the inlet of the SCR catalyst caused by PM filter regeneration events.

In the model-based approach, the module 760 executes an algorithm using each of the plurality of inputs to determine the general SCR catalyst degradation factor 762. In one specific implementation, the algorithm estimates the behavior of the SCR catalyst based on one or more of the plurality of inputs illustrated in FIG. 12 by utilizing any of the various embedded models of the reactions taking place within the SCR catalyst described herein. Generally, the input signals are monitored by the degradation factor generation module 760 to predict the behavior of the SCR catalyst and the corresponding SCR catalyst outlet exhaust properties (e.g., SCR catalyst outlet NO_(x) and NH₃) for a fresh SCR catalyst. The predicted values for SCR catalyst outlet NO_(x) and NH₃ are compared with the actual values for SCR catalyst outlet NO_(x) and NH₃. The actual value for SCR catalyst outlet NO_(x) can be detected by any of various sensors, such as the SCR catalyst outlet NO_(x) sensor 164C (see FIG. 2). Similarly, the actual value for SCR catalyst outlet NH₃ can be detected by any of various sensors, such as the embedded SCR catalyst NH₃ sensor 166B and/or an SCR catalyst outlet NH₃ sensor 166D (see FIG. 2). The differences, i.e., errors, between the predicted and actual values for the SCR catalyst outlet NO_(x) and NH₃ are applied to a predetermined error value versus catalyst degradation factor empirical and/or model based table to determine the general SCR catalyst degradation factor 762.

The SCR catalyst degradation factor module 368 includes a thermal event approach module 764 that utilizes a thermal degradation approach to determine the second SCR catalyst degradation factor 766. In the thermal event approach, the module 764 estimates the second SCR catalyst degradation factor 766 based on a temperature event of the exhaust aftertreatment system 100. As discussed above, temperature events of the exhaust aftertreatment system 100 can accelerate the degradation of the SCR catalyst bed by causing often extreme temperature swings of the SCR catalyst bed. The NH₃ storage capability and NO_(x) conversion capability of the SCR catalyst are impacted by the thermal degradation of the catalyst.

Generally, temperature events include regeneration of the components of the various exhaust aftertreatment system 100. For example, regeneration of the particulate matter filter 142 requires an increase in the temperature of the exhaust gas, which can result in an increase in the temperature of the SCR catalyst bed. Similarly, include regeneration of the SCR catalyst 152 itself to remove hydrocarbon and sulfur byproducts increases the temperature of the SCR catalyst bed. Temperature events can also include desired temperature increases in the exhaust gas resulting from or facilitating improved engine performance and emissions.

The amount of SCR catalyst degradation caused by temperature events is dependent upon the intensity and duration of the events. Generally, the higher the temperatures and the longer the event, the higher the degradation of the SCR catalyst 152. A given temperature event having a specific average temperature and duration can degrade the SCR catalyst 152 by a specific percentage. The relationship between the temperature and duration of temperature events and the amount of degradation can be determined empirically or using modeling techniques. For example, in some specific implementations using a reactor to obtain test data for a small sample of a Fe-Zeolite catalyst, operating the SCR catalyst above 850° C. for a period of 72 hours caused a drop in NO_(x) conversion efficiency of approximately 15% during some engine operating ranges.

Relationship data between temperature, duration, and catalyst degradation for other catalyst types at any of various operating ranges can be obtained using similar testing techniques.

The SCR catalyst degradation factor module 368 includes a system dynamics approach module 768 that utilizes a system dynamics approach to determine the ammonia storage capacity and NO_(x) conversion efficiency SCR catalyst degradation factors 700, 710. In the system dynamics approach, the module 768 generates the ammonia storage capacity SCR catalyst degradation factor 700 based on the control system dynamics properties of the system engine system 10, more particularly, the exhaust aftertreatment system 100. As defined herein, control system dynamics properties include estimated or measured signal time constants, signal damping ratios, and any other properties associated with the various signals of the closed-loop SCR control system, which include sensor signals, aftertreatment control units, urea injection dosing unit, and the control algorithm.

Generally, the system dynamics approach module 768 can include a system properties modulation module (not shown) that requests modulation of at least one parameter of the system. The system dynamics approach module 768 analyzes the results of the modulation to determine the ammonia storage capacity SCR catalyst degradation factor 700. Then, based on the ammonia storage capacity SCR catalyst degradation factor 700, the system dynamics approach module 768 determines the NO_(x) conversion efficiency SCR catalyst degradation factor 710.

In one embodiment, the system dynamics approach module 768 requests modulation of the reductant injection requirement 332 or reductant dosage rate into the exhaust gas stream (see FIG. 8) for the purpose of modulating the SCR catalyst inlet NH₃ signal to match a given SCR catalyst inlet NH₃ signal for which a fresh SCR catalyst outlet NO_(x) signal is known. In certain implementations, the system dynamics approach module 768 communicates a request to the reductant modifier module (see FIG. 16) to modify the reductant modifier requirement 342, which results in a modulation of the reductant injection requirement 332. As the reductant dosage rate is modulated, the degradation factor generation module 760 monitors the SCR catalyst inlet NH₃ 335 and the SCR catalyst outlet NO_(x). In certain implementations, the SCR catalyst outlet NO_(x) is a corrected SCR catalyst outlet NO_(x) calculated in a manner similar to that described above in relation to the corrected tailpipe NO_(x) value 399 and associated corrected tailpipe NO_(x) module 397.

Analyzing the results of modulating the at least one parameter of the system can include comparing any of various properties of the system dynamics during modulation with known properties of the system dynamics for a fresh catalyst at the modulated value for the at least one parameter. In other words, the system dynamics at a given parameter value, e.g., urea dosing rate, for a fresh SCR catalyst and degraded catalyst are compared. The system dynamics for a fresh SCR catalyst are predetermined and stored in a module of the controller 130, such as the SCR catalyst degradation factor module 368. The system dynamics properties are received by a systems properties module, which can be part of the SCR catalyst degradation factor module 368, as input at any time following an initial use of a fresh SCR catalyst. For example, in one embodiment, modulating the reductant dosage rate includes the application of an amplitude and frequency modulation technique to increase or decrease the dosage rate of reductant, e.g., urea, into the exhaust gas stream to create an NH₃ rich or depleted condition in the exhaust entering the SCR catalyst 152. The increased or decreased reductant dosage rate is pre-calibrated to correspond with a given ammonia storage capacity for a fresh SCR catalyst 152.

The system dynamics approach module 768 is configured to execute a phase and measurement algorithm that utilizes orthogonal decomposition of the SCR catalyst inlet NH₃ signal and outlet NO_(x) signal to compute the excitation levels of the signals. In one implementation, the property of the system dynamics being compared can be the time constant or time response of the SCR catalyst inlet NH₃ signal and outlet NO_(x) signal. Generally, the time constants or time responses associated with the SCR catalyst inlet NH₃ and outlet NO_(x) signals for a fresh, non-degraded catalyst is approximately the same. As the SCR catalyst 152 degrades over time, the time constant of the SCR catalyst outlet NO_(x) signal correspondingly changes relative to the SCR catalyst inlet NH₃ signal due to the loss of ammonia adsorption sites associated with a degraded catalyst. Put another way, the time constant of a degraded SCR catalyst outlet NO_(x) signal over time can be different than the predetermined time constant of the SCR catalyst outlet NO_(x) signal of the fresh catalyst.

Any difference in the time constants, e.g., phase difference, indicates a specific drop in the ammonia storage capacity of the SCR catalyst, e.g., a specific drop in ammonia adsorption sites. In other words, based on the phase difference between the SCR catalyst inlet NH₃ and outlet NO_(x) signals, the system dynamics approach module 768 estimates a change in the SCR ammonia storage capacity by comparing a known signal time constant for a fresh catalyst and the signal time constant for the degraded catalyst. Because the change in ammonia storage capacity is based largely on the degradation of the SCR catalyst, the system dynamics approach module 768 assigns a value to the ammonia storage capacity SCR catalyst degradation factor 700 corresponding to the estimated change in the SCR ammonia storage capacity.

Although in the above-described embodiments of the system dynamics approach to determining the SCR catalyst degradation factor, the current system dynamics properties are compared to known properties for a fresh catalyst, in other embodiments, the current system dynamics properties can be compared to known properties for a catalyst having a known level of degradation. For example, based on a comparison between a phase difference between the SCR catalyst inlet NH₃ and outlet NO_(x) signals at a given time, the system dynamics approach module 768 can estimate a change in the SCR ammonia storage capacity, and thus SCR catalyst degradation, by comparing the phase difference at the given time with a stored or known phase difference between the signals at any earlier time at which the amount of degradation of the SCR catalyst is known.

In some instances, the change in time constants is linearly proportional with the ammonia storage capacity change and degradation of the SCR catalyst 152. In other instances, the ammonia storage capacity change and degradation of the SCR catalyst 152 is a non-linear function of the change in time constants. For example, in some implementations, a function relating time constant differentials with SCR catalyst degradation values can be created by experimentally obtaining or virtually sensing a plurality of known SCR catalyst degradation values for given time constants or time constant differentials. The function can be accessible by the system dynamics approach module 768 to estimate the storage capacity degradation of the SCR catalyst 152 based on a known time constant value.

Although the above embodiment utilizes a time constant of SCR catalyst inlet NH₃ and outlet NO_(x) signals as the system dynamics characteristic, in other embodiments, the system dynamics approach module 768 monitors other system dynamics characteristics, such as, for example, time constants or other system dynamics properties associated with the exhaust space velocity and the SCR catalyst bed temperature.

The system dynamics approach utilized by the system dynamics approach module 768 accounts for changes in the storage capacity of the SCR catalyst 152 based on the temperature of the SCR catalyst bed. Generally, the ammonia storage capacity of the SCR catalyst 152 corresponds with the temperature of the SCR catalyst bed. Accordingly, degradation of the SCR catalyst has more or less impact on the NH₃ storage capacity of the SCR catalyst, and thus the storage capacity SCR catalyst degradation factor 700, depending on the SCR catalyst bed temperature. For example, the storage capacity of the SCR catalyst 152 is generally lower for lower SCR catalyst bed temperatures, e.g., less than about 200° C., and generally higher for higher catalyst bed temperatures, e.g., greater than about 500° C. The system dynamics approach accounts for the temperature of the catalyst bed because the properties of the system dynamic properties utilized in the approach are at least partially dependent upon the temperature of the catalyst bed.

The loss of NH₃ adsorption sites associated with the degradation of the SCR catalyst 152 impacts the NO_(x) conversion efficiency of the SCR catalyst. The NO_(x) conversion efficiency of an SCR catalyst is dependent upon the number of NH₃ molecules available to react with NO_(x) in the exhaust gas stream. A loss of NH₃ adsorption sites, i.e., a reduction in the ammonia storage capacity, results in a reduction of the amount of NH₃ molecules available for NO_(x) conversion because fewer NH₃ molecules can absorb to the catalyst wall. Therefore, as the ammonia storage capacity of an SCR catalyst decreases over time due to the degradation of the SCR catalyst, the NO_(x) conversion efficiency of the SCR catalyst correspondingly decreases. In some implementations, the decrease in NO_(x) conversion efficiency is proportional to the decrease in ammonia storage capacity.

Based on the association between ammonia storage capacity and NO_(x) conversion efficiency, the system dynamics approach module 768 determines the NO_(x) conversion efficiency SCR catalyst degradation factor 710. In some implementations, the system dynamics approach module 768 assigns the same value to the NO_(x) conversion efficiency SCR catalyst degradation factor 710 as the ammonia storage capacity SCR catalyst degradation factor 700. However, because the NO_(x) conversion efficiency of an SCR catalyst is not entirely dependent on the ammonia storage capability, in most implementations, the NO_(x) conversion efficiency SCR catalyst degradation factor 710 and the ammonia storage capacity SCR catalyst degradation factor 700 are different. For example, at least some of the NO_(x) passing through the SCR catalyst is converted by reacting with ammonia in the exhaust gas stream, as opposed to ammonia stored on the SCR catalyst. Accordingly, the degradation of the SCR catalyst 152 may not impact the NO_(x) conversion efficiency of the SCR catalyst as much as the ammonia storage capacity of the catalyst. For this reason, even though the NO_(x) conversion efficiency SCR catalyst degradation factor 710 may change along with the ammonia storage capacity SCR catalyst degradation factor 700, in some implementations, the NO_(x) conversion efficiency SCR catalyst degradation factor 710 may not change at the same rate as the ammonia storage capacity SCR catalyst degradation factor 700. In other implementations, the NO_(x) conversion efficiency SCR catalyst degradation factor 710 is proportional to the ammonia storage capacity SCR catalyst degradation factor 700. Generally, for degradation factors defined by a ratio of the condition of a degraded catalyst to the condition of a fresh catalyst, the NO_(x) conversion efficiency SCR catalyst degradation factor 710 is higher than the ammonia storage capacity SCR catalyst degradation factor 700.

In some embodiments, the SCR catalyst degradation factor module 368 is configured to determine a degradation factor of the SCR catalyst 152 using one or more approaches other than the model-based, thermal degradation, and system dynamics approaches. For example, in one implementation, the SCR catalyst degradation factor module 368 monitors performance parameters, such as, for example, a conversion efficiency of specified molecular species, exhaust flow velocity through the SCR catalyst, ambient operating conditions, a cumulative number of duty cycles of the SCR, a distance a vehicle coupled to the SCR catalyst 116, a cumulative time the SCR catalyst is in operation, a number of instances that an SCR catalyst bed temperature exceeds a threshold, a detected ammonia slip at the SCR catalyst outlet compared to an amount of SCR catalyst inlet ammonia and the SCR catalyst bed temperature, a detected ammonia slip at the SCR catalyst outlet compared to an amount of SCR catalyst inlet isocyanic acid and the SCR catalyst bed temperature. The monitored performance parameters are utilized by the degradation factor generation module 760 to determine the general SCR catalyst degradation factor 762.

Generally, one or more of the SCR catalyst degradation factors 700, 710, 762, 766 is used by other modules of the aftertreatment system 100 to estimate the efficiencies and/or capacities of various components of the system. In certain implementations using a ratio of the current SCR catalyst condition to the condition of a new SCR catalyst as the degradation factor, application of an SCR catalyst degradation factor 762 that is less than one results in a reduction of the efficiencies and/or capacities. For general estimations, in some embodiments, the first SCR catalyst degradation factor 762, second SCR catalyst degradation factor 766, or other general SCR catalyst degradation factor can be used. For increased accuracy, in some embodiments, the storage capacity and NO_(x) conversion efficiency SCR catalyst degradation factors 700, 710 are utilized.

For example, in some embodiments, the NO_(x) reduction efficiency module 312 utilizes one of the first and second SCR catalyst degradation factors 762, 766 to estimate the maximum NO_(x) reduction or conversion efficiency of the SCR catalyst 152. However, preferably, the NO_(x) reduction efficiency module 312 utilizes the NO_(x) conversion efficiency SCR catalyst degradation factor 710 to estimate the maximum NO_(x) reduction efficiency of the SCR catalyst 152. Regardless of the degradation factor used, if the degradation factor is less than one, indicating at least some degradation of the catalyst, the maximum NO_(x) reduction efficiency of the SCR catalyst 152 and ammonia addition requirement 326 is reduced, which results in a smaller amount of reductant injected into the exhaust gas stream (see FIG. 5A).

Similarly, in some embodiments, the current NH₃ storage level module 354 utilizes at least one of the first and second SCR catalyst degradation factors 762, 766 to estimate the NH₃ maximum storage capacity 374. However, preferably, the current NH₃ storage level module 354 utilizes the ammonia storage capacity SCR catalyst degradation factor 700 to estimate the NH₃ maximum storage capacity 374 of the SCR catalyst 152. Regardless of the degradation factor used, if the degradation factor is less than one, the NH₃ maximum storage capacity 374 is reduced resulting in a reduction in the amount of reductant injected into the exhaust gas stream, and perhaps an adjustment of the SCR catalyst mode (see, e.g., FIG. 12).

Although in some embodiments, any one of the SCR catalyst degradation factors 700, 710, 762, 766 is used by other modules of the aftertreatment system 100, in other embodiments, a combination of two or more of the degradation factors can be used. For example, the SCR catalyst degradation factor module 368 can average the first and second SCR catalyst degradation factors 762, 766, or all of the degradation factors 700, 710, 762, 766, and the other modules of the aftertreatement system 100 can utilize the average degradation factor in their respective calculations.

Referring back to FIG. 11, according to one embodiment, the current NH₃ storage level module 354 determines the estimated current NH₃ storage level 370 by utilizing, at least in part, the current condition, e.g., degradation, of the SCR catalyst bed, the size and properties of the SCR catalyst bed, and the ammonia flux entering the SCR catalyst. Referring to FIG. 13, and according to one exemplary embodiment, the NH₃ storage level module 354 utilizes the schematic flow chart 500 to determine the current NH₃ storage level 370 on the SCR catalyst 152. The reductant target module 330 is operable to determine the reductant injection requirement 332, e.g., urea dosing rate, at 510. Alternatively, the current NH₃ storage level module 354 is communicable in data receiving communication with the reductant delivery mechanism 190 for receiving the current reductant dosing rate 383. The SCR catalyst bed temperature sensor 124C senses, or a bed temperature module estimates, the temperature of the SCR catalyst bed temperature at 520.

Based at least partially on the temperature of the SCR catalyst bed as determined at 520, the NH₃ maximum storage capacity 374 is generated by the current NH₃ storage level module 354 at 530. The NH₃ maximum storage capacity 374 is dependent on the temperature of the SCR catalyst bed and can be determined by comparing the SCR catalyst bed temperature against a pre-calibrated look-up table. The urea dosing rate, which corresponds to the ammonia flux entering the SCR catalyst 152, and SCR catalyst bed temperature are used to determine an NH₃ fill-up or adsorption time constant and the SCR catalyst bed temperature and NO_(x) flux are used to determine an NH₃ removal or desorption time constant. The time constants can be retrieved from respective look-up tables 540, 550 stored on, for example, the current NH₃ storage level module 354.

A determination of the SCR catalyst mode is made at 560. Based on whether the SCR catalyst 152 is in an NH₃ fill-up mode or an NH₃ removal mode, the corresponding time constant (τ) is used to calculate the current NH₃ storage level (NH₃Storage) at 570 according to the following first order dynamics equation:

$\begin{matrix} {{{NH}_{3}{Storage}} = {{NH}_{3}{{Storage}_{MAX}\left( \frac{1}{{\tau\; s} + 1} \right)}}} & (16) \end{matrix}$ where NH₃Storage_(MAX) is the NH₃ maximum storage capacity 374 of the SCR catalyst 152 and s is the complex variable used for Laplace transforms. In other words, if it is determined at 560 that more ammonia should be stored on the SCR catalyst 152, the NH₃ adsorption time constant determined at 540 is used in Equation 16 to determine the current NH₃ storage level 370. Alternatively, if it is determined at 560 that ammonia should be removed from the SCR catalyst 152, the NH₃ desorption time constant determined at 550 is used in Equation 16 to determine the current NH₃ storage level 370. Accordingly, the current NH₃ storage level 370 is at least partially based on the ammonia flux, temperature of the catalyst and degradation of the catalyst.

In at least one embodiment, the storage mode, e.g., fill-up or removal mode, of the SCR catalyst 152 is determined by the NH₃ storage module 350 by comparing the NH₃ maximum storage capacity 374 with the current NH₃ storage level 370. If the NH₃ maximum storage capacity 374 is less than the current NH₃ storage level 370 then the SCR catalyst 152 is in the desorption mode. Similarly, if the NH₃ maximum storage capacity 374 is more than the current NH₃ storage level 370 then the SCR catalyst 152 is in the adsorption mode.

The look-up tables utilized at 540, 550 include a listing of the adsorption and desorption time constants, respectively, corresponding to various possible urea dosing rates and SCR catalyst bed temperatures. In certain implementations, the adsorption time constants can be calibrated using steady-state testing. For example, the engine 11 can be run at specific steady state modes such that the temperature of SCR catalyst bed reaches and is held at a specific temperature corresponding to each mode. Prior to reaching each mode, the SCR catalyst 152 is clean such that the catalyst bed does not contain stored ammonia, i.e., the amount of NO_(x) coming out of the engine is the same as the amount of NO_(x) coming out of the SCR catalyst. For each respective mode, the reductant target module 330 is operable to communicate to the reductant delivery mechanism 190 to inject an amount of reductant necessary to achieve 100% conversion of NO_(x). The amount of reductant can vary for different stoichiometric reactions rates ranging, for example, between about 0.5 to about 2.0. The amount of time between the initial reductant dosing and ammonia slippage from the SCR catalyst 152 is determined for each mode at each stoichiometric reaction dosing rate and used to calibrate the adsorption time constants in the NH₃ fill-up time constant table.

The desorption time constants in the NH₃ removal time constant table can be calibrated during the same test used for calibrating the adsorption time constants. For example, after NH₃ begins to slip from the SCR catalyst 152 as described above, the NH₃ slip and NO_(x) leaving the SCR catalyst are monitored until they stabilize or become constant. Once the NH₃ slip and SCR catalyst outlet NO_(x) are stable, the urea dosing is discontinued and the amount of time between discontinuation of urea dosing and the SCR catalyst outlet NO_(x) to equal the engine outlet NO_(x) is determined for each mode at each stoichiometric reaction dosing rate.

If desired, the adsorption and desorption time constants can be further calibrated to compensate for transient operation of the engine 11. For example, the Fourier Transform Infrared (FTIR) measurements of ammonia slip values and the time between the beginning of a transient FTP cycle and slippage from the SCR catalyst can be used to fine-tune the adsorption and desorption time constants. More specifically, the time constants can be adjusted based on a least squares approach that can provide the best first order model fit to the transient data.

The target NH₃ storage level module 356 is operable to determine a target NH₃ storage level based at least in part on the NH₃ maximum storage capacity 374 determined by the current NH₃ storage level module 354. Generally, the target NH₃ storage level module 356 determines the target NH₃ storage level by multiplying the NH₃ maximum storage capacity 374 by an ammonia storage level fraction. The ammonia storage level fraction can be any of various fractions, such as fifty percent, seventy-five percent, ninety percent, and one-hundred percent. The ammonia storage level fraction is determined based at least partially on the SCR catalyst degradation factor and user defined maximum allowable ammonia slip.

Once the current NH₃ storage level 370 and the target NH₃ storage level are determined, the NH₃ storage module 350 utilizes the current NH₃ storage level 370 as feedback and compares the current NH₃ storage level and the target NH₃ storage level. If the current NH₃ storage level is less than the target NH₃ storage level, the ammonia storage modifier 352 is set to a positive value. If the current NH₃ storage level 370 is more than the target NH₃ storage level, the ammonia storage modifier 352 is set to a negative value. The positive and negative values can vary depending on how much less or more the current NH₃ storage level 370 is compared to the target NH₃ storage level. The ammonia storage modifier 352 is communicated to the ammonia target module 310 (see FIG. 5). An ammonia storage modifier 352 with a positive value indicates to the ammonia target module 310 that the ammonia addition requirement 326 should be correspondingly increased. In contrast, an ammonia storage modifier 352 with a negative value indicates to the ammonia target module 310 that the ammonia addition requirement 326 should be correspondingly decreased.

The amount of NH₃ storage on the catalyst 152 can be controlled by controlling any of various inputs into the SCR system 150. For example, referring again to FIG. 13, the amount of ammonia storage on the SCR catalyst 152 is dependent on the following separately controllable factors: the urea dosing rate, the SCR catalyst bed temperature, and the SCR catalyst maximum capacity. Accordingly, the controller 130 can be operable to selectively or cooperatively control the current NH₃ storage level on the SCR catalyst 152.

The ammonia storage modifier 352 also can be adjusted according to the current NH₃ storage slip 372, the presence or absence of an AMOX catalyst, such as AMOX catalyst 160, and if an AMOX catalyst is used, the conversion capability 382 of the AMOX catalyst.

According to one embodiment, the SCR catalyst ammonia slip module 369 determines the estimated current NH₃ slip 372 from the SCR catalyst 152 by utilizing, at least in part, the ammonia and NO_(x) flux entering the catalyst, the size and properties of the SCR catalyst bed, and the ratio of NO to NO₂. Referring to FIG. 14, and according to one exemplary embodiment, the ammonia slip module 369 utilizes the schematic flow chart 600 to determine the current NH₃ slip 372 from the SCR catalyst 152. The amount of NO_(x) at the inlet of the SCR catalyst 152 is determined at 610 and the amount of NO_(x) at the outlet of the SCR catalyst is determined at 614. The NO_(x) inlet amount can be sensed by the NO_(x) sensor 164A and the NO_(x) outlet amount can be sensed by the NO_(x) sensor 164C or NO_(x) sensor 164D. To account for any degradation of the sensor 164D, the output of the NO_(x) sensor 164D can be corrected as described above in relation to corrected tailpipe NO_(x) module 362. The ratio of NO to NO₂ in the exhaust gas stream at the inlet of the SCR catalyst 152 is determined at 612 and the ratio of NO to NO₂ in the exhaust gas stream at the outlet of the SCR catalyst is determined at 616. In some implementations, the SCR catalyst NO₂/NO_(x) ratio module 366 is operable to determine the NO to NO₂ ratios at the inlet and outlet of the SCR catalyst 152, respectively.

At 620, the amount of ammonia consumed within the SCR catalyst 152 is calculated based on the net loss, e.g., conversion, of NO and NO₂ from the exhaust gas stream. In some implementations, the calculation is performed by the current NH₃ storage level module 354. Based at least partially on the flow of NH₃ into the SCR catalyst 152 determined at 630 and the amount of ammonia consumed within the SCR catalyst 152, the excess amount of NH₃ within the SCR catalyst is estimated at 640. As described above, the amount of NH₃ flowing into the SCR catalyst 152 can be determined by utilizing flow chart 400 of FIG. 10.

Further, based at least partially on the current NH₃ storage level 370 determined at 650, the flow rate of the exhaust gas stream into and through the SCR catalyst 152 determined at 652, and the temperature of the SCR catalyst bed determined at 653, the amount of ammonia desorbed from the bed of the SCR catalyst 152 is estimated at 660. Generally, desorption of ammonia occurs when there is a specific increase in the temperature of the SCR catalyst bed. The amount of temperature increase necessary to effect desorption of ammonia is at least partially dependent on the condition and type of SCR catalyst being used. As shown in FIG. 11, the current NH₃ storage level module 354 can include the desorbed NH₃ module 375, which is operable to estimate the amount of ammonia desorbed from the bed of the SCR catalyst 152. In certain implementations, the NH₃ storage level module 354 estimates the amount of ammonia desorbed from the SCR catalyst bed based on the excess NO_(x) flux available for reduction reaction on the SCR catalyst surface.

Based at least partially on the excess amount of NH₃ within the SCR catalyst 152, the amount of NH₃ desorbed from the SCR catalyst bed, and the amount of NH₃ stored on the SCR catalyst relative to the NH₃ maximum storage capacity 374 of the catalyst, i.e., the fraction of the SCR catalyst occupied by stored ammonia, the amount of NH₃ slipping from the SCR catalyst is estimated at 680. The amount of NH₃ slipping from the SCR catalyst 152 is equal to the sum of the excess amount of NH₃ determined at 640 and the desorbed amount of NH₃ determined at 660. The fraction of the SCR catalyst occupied by stored ammonia is determined at 670 by dividing the NH₃ stored on the catalyst as determined at 650 by the NH₃ maximum storage capacity determined, for example, at 530 of flow diagram 500. Generally, if the total amount of NH₃ stored on the SCR catalyst 152 is greater than the NH₃ maximum storage capacity 374, i.e., the ammonia stored fraction determined at 670 is greater than one, then ammonia slip from the catalyst is occurring and the amount of slip is determined at 680. If the total amount of NH₃ within the SCR catalyst is less than the NH₃ maximum storage capacity 374, i.e., the ammonia stored fraction is less than one, then ammonia slip is not occurring and the amount of ammonia slip is not calculated at 680. In other words, the model used to compute the ammonia slip at 680 does not become active until the SCR catalyst 152 is full with ammonia, or the SCR catalyst bed temperature and rate of increase of the SCR catalyst bed temperatures are above predetermined thresholds.

The amount of NH₃ slip from the catalyst 152 can be controlled by controlling any of various inputs into the SCR system 150. For example, referring to FIG. 14, the amount of ammonia slip from the SCR catalyst 152 is dependent on the following separately controllable factors: the amount of NH₃ flowing into the SCR catalyst as determined at 630; the exhaust flow rate as determined at 652; and the current NH₃ storage level as determined using flow chart 500. Accordingly, the controller 130 can be operable to selectively or cooperatively control the NH₃ slip from the SCR catalyst.

If the current NH₃ storage slip 372 is relatively high, such as when the temperature of the SCR catalyst bed exceeds a predetermined level, then the NH₃ storage module is operable to decrease the ammonia storage modifier 352. In contrast, if the current NH₃ storage slip 372 is relatively low, then the NH₃ storage module is operable to increase or hold steady the ammonia storage modifier 352.

AMOX Ammonia Conversion Module

According to one embodiment shown in FIG. 15, the AMOX NH₃ conversion module 380 determines an AMOX NH₃ conversion capability or efficiency 382, a tailpipe NH₃ slip 384 and an AMOX catalyst thermal mass 385. Generally, the NH₃ conversion capability 382 represents an estimate of the ability of the AMOX catalyst 160 to convert NH₃ to N₂ and other less harmful or less noxious components. The tailpipe NH₃ slip 384 represents an estimate of the amount of NH₃ exiting the AMOX catalyst 160. As will be described in more detail below, the AMOX thermal mass 385 is a measure of the AMOX catalyst's ability to conduct and store heat.

The AMOX NH₃ conversion module 380 receives input regarding the exhaust gas flow rate 700 entering the AMOX catalyst 160 and the amount of NH₃ entering the AMOX catalyst. In some implementations, the exhaust gas flow rate 700 is determined by the SCR catalyst inlet exhaust properties module 358 of current NH₃ storage level module 354 (see FIG. 11) or other similar module. The amount of NH₃ entering the AMOX catalyst 160 can be represented by an NH₃ input 712 and/or the current NH₃ slip 372. More specifically, in some implementations, the AMOX NH₃ conversion module 380 is communicable in data receiving communication with the current NH₃ storage level module 354 to receive the current NH₃ slip 372. In these implementations, the amount of NH₃ entering the AMOX catalyst 160 can be set to the current NH₃ slip 372. In some implementations, the control system 150 can include an NH₃ sensor between the SCR catalyst 152 and the AMOX catalyst 160. In these implementations, the amount of NH₃ entering the AMOX catalyst 160 can be set to the output of the NH₃ sensor. Alternatively, in certain instances, the amount of NH₃ entering the AMOX catalyst 160 can be set to a combination of the current NH₃ slip 372 and the output of the NH₃ sensor, such as an average of the current NH₃ slip 372 and the output of the NH₃ sensor. The AMOX NH₃ conversion module 380 can also be communicable in data receiving communication with various other sensors, such as temperature sensors 124D, 124E and NO_(x) sensor 164C.

The AMOX NH₃ conversion module 380 includes several modules including, but not limited to, an AMOX catalyst bed temperature module 386, an NO₂/NO_(x) ratio module 387, an AMOX catalyst degradation module 388, and a tailpipe NH₃ slip target module 389.

The AMOX catalyst bed temperature module 386 is operable to estimate the temperature of the AMOX catalyst bed. In one implementation, the AMOX catalyst bed temperature module 386 utilizes the input from the temperature sensors 124D, 124E to determine the difference between the temperature of the exhaust at the inlet of the AMOX catalyst 160 and the temperature of the exhaust at the outlet of the AMOX catalyst. Based at least partially on the temperature differential and mass flow rate properties of the exhaust gas stream, the AMOX catalyst bed temperature module 386 calculates the temperature of the AMOX catalyst bed. Alternatively, or in addition to estimating the AMOX catalyst bed temperature as described above, the SCR system 150 can include a temperature sensor (not shown) coupled to the AMOX catalyst 160. The AMOX catalyst bed temperature module 386 can utilize the output of the AMOX catalyst temperature sensor to determine the temperature of the AMOX catalyst bed.

Similar to the SCR catalyst NO₂/NO_(x) ratio module 366 of the current NH₃ storage level module 354, the NO₂/NO_(x) ratio module 387 of the AMOX NH₃ conversion module 380 is operable to determine the ratio of NO₂ to NO_(x) according to Equation 1 above, where NO₂ is the amount of nitrogen dioxide at the inlet of the AMOX catalyst 160 and NO is the amount of nitrogen oxide at the inlet of the AMOX catalyst as sensed by the NO_(x) sensor 164C.

Similar to the SCR catalyst degradation factor module 368 of current NH₃ storage level module 354, the AMOX catalyst degradation module 388 is operable to determine an AMOX catalyst degradation factor indicating the condition of the AMOX catalyst. In certain implementations, the catalyst degradation factor is determined by an algorithm that compares the conversion efficiency of the “aged” AMOX catalyst at predetermined engine operating conditions and urea dosing rates with the conversion efficiency of a “fresh” AMOX catalyst under the same predetermined conditions and dosing rates.

The tailpipe NH₃ slip target module 389 is operable to determine a tailpipe NH₃ slip target, i.e., the desired amount of NH₃ allowed to exit the AMOX catalyst 160. The tailpipe NH₃ slip target is based at least partially on a desired average amount of NH₃ slip from the AMOX catalyst and/or a desired maximum amount of NH₃ slip from the AMOX catalyst. In some instances, both the desired average amount of NH₃ slip from the AMOX catalyst and desired maximum amount of NH₃ slip from the AMOX catalyst are used to ensure that actual tailpipe slip levels remain below a human detectable threshold. Further, the tailpipe NH₃ slip target can be based on other factors, such as current emissions standards and customer-based specifications.

Based at least partially on at least one of the flow rate of exhaust, NO_(x), and ammonia entering the AMOX catalyst 160, the temperature of the AMOX catalyst bed, the ratio of NO₂/NO_(x) at the inlet of the AMOX catalyst, the catalyst degradation factor, and the tailpipe NH₃ slip target, the AMOX NH₃ conversion module 380 estimates the AMOX NH₃ conversion capability 382, the tailpipe NH₃ slip 384, and the AMOX catalyst thermal mass 385. For example, in some implementations, the AMOX NH₃ conversion capability 382 and the tailpipe NH₃ slip 384 are dependent on the amount of NO_(x) entering the AMOX catalyst, the temperature of the AMOX catalyst, and a space velocity of the AMOX catalyst. Further, in some instances, the AMOX catalyst thermal mass 385 is based at least partially on the geometric dimensions of the AMOX catalyst, and the material properties of the AMOX catalyst, such as the thermal conductivity and volumetric heat capacity of the AMOX catalyst. In some instances, the AMOX NH₃ conversion capability 382, the tailpipe NH₃ slip 384, and the AMOX catalyst thermal mass 385 can be estimated by accessing a multi-dimensional, pre-calibrated look-up table stored on the controller 130.

Generally, the higher the AMOX catalyst conversion capability 382, the more tolerance the SCR system 150 has to NH₃ slipping from the SCR catalyst 152. Accordingly, if the AMOX catalyst conversion capability 382 is relatively high, more NH₃ can be allowed to slip from the SCR catalyst 152. However, with more NH₃ slipping from the SCR catalyst 152, more NH₃ storage sites on the surface of the SCR catalyst 152 may be vacant, thus requiring an increase in the ammonia addition requirement 326. In such an instance, the NH₃ storage module 350 can increase the ammonia storage modifier 352, which in turn can increase the ammonia addition requirement 326. In contrast, when the AMOX catalyst conversion capability 382 is relatively low, less NH₃ slippage from the SCR catalyst 152 is tolerated, resulting in less NH₃ removed from storage on the SCR catalyst. If more NH₃ slips from the SCR catalyst 152 and the AMOX catalyst conversion capability 382 is relatively low, the tailpipe NH₃ slip may correspondingly increase. Therefore, in these instances, the NH₃ storage module 350 can decrease or hold steady the ammonia storage modifier 352 to decrease or hold-steady the ammonia addition requirement 326, and/or the AMOX NH₃ conversion module 380 can modulate the effectiveness of the AMOX catalyst 160, such that tailpipe NH₃ slip is controlled.

In some implementations, the AMOX catalyst thermal mass value 385 is dependent on the material properties of the AMOX catalyst bed, such as thermal conductivity and volumetric heat capacity. Generally, the thermal mass 385 is a measure of the AMOX catalyst's ability to conduct and store heat. The AMOX NH₃ conversion module 380 can communicate the AMOX catalyst thermal mass value 385 to the NH₃ storage module 350, which can use the thermal mass value in its determination of the ammonia storage modifier 352.

As described above, the AMOX NH₃ conversion capability and AMOX catalyst thermal mass 385 is communicated to and processed by various other modules of the controller 130. For example, the AMOX NH₃ conversion capability 382 and AMOX catalyst thermal mass 385 is received by the NH₃ storage module 350 and used to determine the ammonia storage modifier 352 (see FIG. 10). Further, the AMOX NH₃ conversion capability 382 is used by the corrected tailpipe NO_(x) module 399 to determine the tailpipe NO_(x) feedback value 399 (see FIG. 17).

The tailpipe NH₃ slip 384 determined by the AMOX embedded model NH₃ conversion module 380 can be communicated to other modules of the controller 130. For example, the determined tailpipe NH₃ slip 384 can be communicated to the reductant modifier module 390 (see FIG. 16) and corrected tailpipe NO_(x) module 397 (see FIG. 17) to replace or supplement the tailpipe NH₃ slip measurement input communicated from the NH₃ sensor 166C. For example, in certain instances, the input value for the tailpipe NH₃ into the modules 390, 397 can be an average of the determined tailpipe NH₃ slip 384 and the tailpipe NH₃ slip measurement from the sensor 166C to provide a more accurate indication of the actual amount of NH₃ slipping from the tailpipe.

Reductant Modifier Module

Referring to FIG. 16, the reductant modifier module 390 is operable to determine a reductant modifier requirement 342 based at least in part on whether any of various reductant limiting conditions have been met. The reductant modifier module 390 includes a reductant modifier conditions module 394 and an SCR catalyst inlet exhaust properties module 395. Generally, the reductant modifier module 390 is operable to either reduce reductant dosing, prevent reductant dosing or leave reductant dosing unchanged when certain predetermined conditions of the exhaust aftertreatment system 100 are met.

The reductant modifier conditions module 394 is operable to monitor the operating conditions of the engine system 10 and determine if one or more reductant limiting conditions are met. In some embodiments, the reductant limiting conditions include, but are not limited to, an exhaust gas temperature limit, an ammonia slip reductant rate limit, and an SCR catalyst bed temperature limit.

Reductant dosing at high exhaust gas temperatures can cause cyanuric acid and polymers (e.g., melamine) to form on the injector and exhaust pipe walls, which can lead to performance degradation of and damage to the system. For example, the formation of melamine can clog the nozzle. To prevent cyanuric acid from forming, the reductant modifier module 390, including the reductant modifier conditions module 394, monitors the exhaust gas temperature and prevents reductant dosing, e.g., via instructions in the reductant modifier requirement 342, if the exhaust gas temperature exceeds a predetermined exhaust gas temperature limit. The current exhaust gas temperature can be sensed by at least one of the temperature sensors, e.g., exhaust temperature sensor 124C and/or predicted by an SCR catalyst inlet exhaust properties module 395 similar to module 358.

Reductant dosing at high SCR catalyst storage levels and SCR catalyst bed temperature ramps can cause ammonia to slip from the SCR catalyst 152. To reduce ammonia slip in these situations, the reductant modifier module 390 monitors the current NH₃ storage level 370 and the modulations of the SCR catalyst bed temperature as sensed by the temperature sensor 124D (or predicted by an SCR catalyst bed temperature module as described above). If the current NH₃ storage level 370 exceeds a predetermined NH₃ storage level associated with NH₃ slip, or if the modulation in SCR catalyst bed temperature exceeds a predetermined SCR catalyst bed temperature change, then the reductant modifier module reduces the reductant dosing rate, e.g., via instructions in the reductant modifier requirement, such that NH₃ slip from the SCR catalyst 152 is controlled.

The reductant modifier module 390 is also operable to prevent reductant dosing in the event a specific component or components of the SCR system 150 has malfunctioned or is otherwise not ready for operation.

Corrected Tailpipe NO_(x) Module

Referring to FIG. 17, the corrected tailpipe NO_(x) module 397 of the controller 130 is operable to determine the corrected tailpipe NO_(x) value 399. The corrected tailpipe NO_(x) module 397 is communicable in data receiving communication with the tailpipe NO_(x) sensor 164D and tailpipe NH₃ sensor 166C. The corrected tailpipe NO_(x) module 397 is also communicable in data receiving communication with the current NH₃ storage level module 354 to receive the estimated current NH₃ slip 372 or the estimated amount of NH₃ exiting the SCR catalyst 152. Further, the corrected tailpipe NO_(x) module 397 is communicable in data receiving communication with the AMOX NH₃ conversion module 380 to receive the AMOX NH₃ conversion capability 382. The corrected tailpipe NO_(x) module 397 also includes a sensor degradation module 398 that is operable to determine a tailpipe NO_(x) sensor degradation factor based at least partially on the type of sensor, age of sensor, and operating conditions of the engine system 10. In some instances, the tailpipe NO_(x) sensor degradation factor is determined by an algorithm that compares the NO_(x) sensor measurements at pre-determined operating conditions having known NO_(x) values. The degradation factor indicates an amount, e.g., a percentage, the measured NO_(x) sensor value should be adjusted to account for degradation of the NO_(x) sensor and inaccuracies associated with the degraded NO_(x) sensor measurements. In some implementations, the corrected tailpipe NO_(x) value is about is about 10% higher than the measured tailpipe NO_(x) value.

The corrected tailpipe NO_(x) module 397 processes the sensed tailpipe NO_(x) amount, the sensed tailpipe NH₃ amount, the estimated NH₃ slip 372, the NO_(x) sensor degradation factor, and the AMOX conversion capability 382 to determine the corrected tailpipe NO_(x) value 399. The corrected tailpipe NO_(x) value 399 can replace the sensed amount of NO_(x) detected by the tailpipe NO_(x) sensor 164D in the reductant modifier requirement 342 calculation by the reductant modifier module 390 for a more accurate indication of the amount of NO_(x) leaving the tailpipe and a more accurate reductant modifier requirement. Additionally, the corrected tailpipe NO_(x) value 399 can be communicated to and processed by the current NH₃ storage level module 354. In embodiments of an engine system not having an AMOX catalyst, the AMOX NH₃ conversion capability 382 is not a factor in the determination of the corrected tailpipe NO_(x) value 399. In such instances, the corrected tailpipe NO_(x) value is a corrected SCR catalyst outlet NO_(x) value.

Exemplary Method for Reducing NO_(x) Emissions

Referring to FIG. 18, and according to one representative embodiment, a method 800 for reducing NO_(x) emissions using ammonia storage on an SCR catalyst is shown. The method 800 starts at 802 and includes determining 804 a NO_(x) reduction requirement. In some implementations, determining 804 a NO_(x) reduction requirement includes operating the NO_(x) reduction target module 300 to estimate the NO_(x) reduction requirement 304. The method 800 also includes determining 806 an ammonia addition requirement. In some implementations, determining 806 an ammonia addition requirement includes operating the ammonia target module 310 to estimate the ammonia addition requirement 326. The method 800 further includes determining 808 an ammonia storage modifier. In some implementations, determining 808 an ammonia storage modifier includes operating the NH₃ storage module 350 to estimate the ammonia storage modifier 352.

After an ammonia storage modifier is determined, the method 800 includes comparing 810 the ammonia storage modifier to a predetermined value, such as zero. If the ammonia storage modifier is greater than or less than the predetermined value, then the method 800 includes adjusting 812, such as by adding, the ammonia addition requirement determined at 808 by an amount corresponding to the ammonia storage modifier amount. If the ammonia storage modifier is approximately equal to the predetermined value, then the ammonia addition requirement determined at 808 is not adjusted. The method 800 includes determining 814 a reductant injection requirement 814 based on either the ammonia addition requirement determined at 808 or the adjusted addition requirement determined at 812. In some implementations, determining 814 a reductant injection requirement includes operating the reductant target module 330 to calculate the reduction injection requirement 332. The method 800 can also include determining 815 an AMOX catalyst NH₃ conversion capability 382 by operation of the AMOX NH₃ conversion module 380.

The method 800 further includes determining 816 a reductant modifier. In some implementations, determining 816 a reductant modifier includes operating the reductant modifier module 390 to calculate the reductant modifier requirement 342. After a reductant modifier is determined, the method 800 includes comparing 820 the reductant modifier to a predetermined value, such as zero. If the reductant modifier is greater than or less than the predetermined value, then the method 800 includes adjusting 822 the reductant injection requirement determined at 816 by an amount corresponding to the reductant modifier amount. If the reductant modifier is approximately equal to the predetermined value, then the reductant injection requirement determined at 808 is not adjusted. The method includes injecting 824 an amount of reductant corresponding to the reductant injection requirement determined at either 816 or 822 into the exhaust gas stream.

The schematic flow chart diagrams and method schematic diagrams described above are generally set forth as logical flow chart diagrams. As such, the depicted order and labeled steps are indicative of representative embodiments. Other steps and methods may be conceived that are equivalent in function, logic, or effect to one or more steps, or portions thereof, of the methods illustrated in the schematic diagrams. Additionally, the format and symbols employed are provided to explain the logical steps of the schematic diagrams and are understood not to limit the scope of the methods illustrated by the diagrams. Although various arrow types and line types may be employed in the schematic diagrams, they are understood not to limit the scope of the corresponding methods. Indeed, some arrows or other connectors may be used to indicate only the logical flow of a method. For instance, an arrow may indicate a waiting or monitoring period of unspecified duration between enumerated steps of a depicted method. Additionally, the order in which a particular method occurs may or may not strictly adhere to the order of the corresponding steps shown.

The present invention may be embodied in other specific forms without departing from its spirit or essential characteristics. The described embodiments are to be considered in all respects only as illustrative and not restrictive. The scope of the invention is, therefore, indicated by the appended claims rather than by the foregoing description. All changes which come within the meaning and range of equivalency of the claims are to be embraced within their scope. 

1. An apparatus for determining the degradation of a selective catalytic reduction (SCR) catalyst of an engine exhaust aftertreatment system, comprising: a system properties module configured to store at least one system dynamics property value of the exhaust system at a first time and receive the at least one system dynamics property value of the exhaust aftertreatment system at a second time subsequent to the first time; a system dynamics module configured to determine a storage capacity of the SCR catalyst based on a comparison between the at least one system dynamic property value at the first time and the at least one system dynamic property value at the second time; and an SCR catalyst degradation factor module configured to determine an ammonia storage capacity SCR catalyst degradation factor and an NO_(x) conversion efficiency SCR catalyst degradation factor based at least partially on the storage capacity of the SCR catalyst.
 2. The apparatus of claim 1, wherein the at least one system dynamics property value comprises a difference between an SCR catalyst inlet NH₃ signal and an SCR catalyst outlet NO_(x) signal.
 3. The apparatus of claim 1, wherein the at least one system dynamics property value comprises a difference between a time constant of an SCR catalyst inlet NH₃ signal and a time constant of an SCR catalyst outlet NO_(x) signal.
 4. The apparatus of claim 1, wherein the system dynamics module is configured to modulate a parameter of the exhaust aftertreatment system at approximately the second time to achieve a parameter value corresponding with the at least one system dynamic property value of the exhaust system at the first time.
 5. The apparatus of claim 4, wherein the modulated parameter comprises a urea dosing rate or NO_(x) exiting an internal combustion engine coupled to the engine exhaust aftertreatment system.
 6. The apparatus of claim 1, wherein the ammonia storage capacity SCR catalyst degradation factor comprises a first SCR catalyst degradation factor and the NO_(x) conversion efficiency SCR catalyst degradation factor comprises a second SCR catalyst degradation factor, and wherein the SCR catalyst degradation factor module is configured to determine a third SCR catalyst degradation factor based at least partially on a comparison between at least one predicted SCR catalyst outlet parameter value for a fresh SCR catalyst at given exhaust aftertreatment operating conditions and at least one measured SCR catalyst outlet parameter value for the SCR catalyst at the given exhaust aftertreatment operating conditions.
 7. The apparatus of claim 6, wherein the SCR catalyst degradation factor module determines the third SCR catalyst degradation factor by applying the difference between the at least one predicted SCR catalyst outlet parameter value and the at least one measured SCR catalyst outlet parameter value to a predetermined parameter value difference versus catalyst degradation factor table.
 8. The apparatus of claim 6, wherein the at least one SCR catalyst outlet parameter value comprises SCR catalyst outlet NO_(x) and NH₃ values, and wherein the SCR catalyst degradation factor module is configured to determine the predicted SCR catalyst outlet NO_(x) and NH₃ values based at least partially on an SCR catalyst inlet exhaust gas temperature, an SCR catalyst inlet exhaust gas space velocity, an SCR catalyst bed temperature, an SCR catalyst inlet NO_(x) value, an SCR catalyst inlet NO₂/NO_(x) ratio, an SCR catalyst inlet NH₃ value, an SCR catalyst inlet isocyanic acid value, and an SCR catalyst outlet exhaust gas temperature value.
 9. The apparatus of claim 1, wherein the ammonia storage capacity SCR catalyst degradation factor comprises a first SCR catalyst degradation factor and the NO_(x) conversion efficiency SCR catalyst degradation factor comprises a second SCR catalyst degradation factor, and wherein the SCR catalyst degradation factor module is configured to determine a third SCR catalyst degradation factor based at least partially on an exhaust temperature increase event within the exhaust aftertreatment system.
 10. The apparatus of claim 9, wherein the exhaust temperature increase event is defined by an exhaust temperature increase amount and an exhaust temperature increase duration, the third SCR catalyst degradation factor being associated with an exhaust temperature increase amount and duration combination.
 11. The apparatus of claim 1, further comprising an ammonia storage capacity module configured to determine a maximum ammonia storage capacity of the SCR catalyst based at least partially on the ammonia storage capacity SCR catalyst degradation factor.
 12. The apparatus of claim 1, further comprising an NO_(x) conversion efficiency module configured to determine a maximum NO_(x) conversion efficiency of the SCR catalyst based at least partially on the NO_(x) conversion efficiency SCR catalyst degradation factor.
 13. A method for determining the degradation of a selective catalytic reduction (SCR) catalyst of an engine exhaust aftertreatment system, comprising: modulating an SCR catalyst inlet exhaust condition to achieve a predefined SCR catalyst inlet exhaust condition value; monitoring an SCR catalyst inlet exhaust condition signal and an SCR catalyst outlet exhaust condition signal; comparing a system dynamics property of the SCR catalyst inlet exhaust condition signal and a corresponding system dynamics property of the SCR catalyst outlet exhaust condition signal; determining a ammonia storage capacity of the SCR catalyst based at least partially on a difference between the system dynamics property of the first SCR catalyst exhaust condition signal and the corresponding system dynamics property of the second SCR catalyst outlet exhaust condition signal; and determining an SCR catalyst degradation factor based at least partially on the ammonia storage capacity.
 14. The method of claim 13, wherein the SCR catalyst degradation factor comprises an ammonia storage capacity SCR catalyst degradation factor.
 15. The method of claim 13, further comprising correlating the maximum ammonia storage capacity of the SCR catalyst with a NO_(x) conversion efficiency of the SCR catalyst, wherein the SCR catalyst degradation factor comprises an NO_(x) conversion efficiency SCR catalyst degradation factor.
 16. The method of claim 13, wherein the system dynamics property of the SCR catalyst inlet exhaust condition signal comprises a time constant of the SCR catalyst inlet exhaust condition signal and the system dynamics property of the SCR catalyst outlet exhaust condition signal comprises a time constant of the SCR catalyst outlet exhaust condition signal.
 17. The method of claim 13, wherein the SCR catalyst inlet exhaust condition comprises the amount of NH₃ entering the SCR catalyst, and wherein modulating the amount of NH₃ entering the SCR catalyst comprises modulating the flow rate of a reductant injected into the exhaust upstream of the SCR catalyst.
 18. The method of claim 17, wherein the SCR catalyst inlet exhaust sensor signal comprises an SCR catalyst inlet NH₃ sensor signal and the SCR catalyst outlet exhaust sensor signal comprises an SCR catalyst outlet NO_(x) sensor signal.
 19. The method of claim 17, wherein modulating the flow rate of the reductant injected into the exhaust comprises modulating the flow rate to a predefined flow rate corresponding with a given ammonia storage capacity of the SCR catalyst.
 20. The method of claim 13, wherein the SCR catalyst degradation factor comprises a first SCR catalyst degradation factor, the method further comprising determining a second SCR catalyst degradation factor based at least partially on an SCR catalyst inlet exhaust gas temperature, an SCR catalyst inlet exhaust gas space velocity, an SCR catalyst bed temperature, an SCR catalyst inlet NO_(x) value, an SCR catalyst inlet NO₂/NO_(x) ratio, an SCR catalyst inlet NH₃ value, an SCR catalyst inlet isocyanic acid value, and an SCR catalyst outlet exhaust gas temperature value.
 21. The method of claim 20, further comprising determining a third SCR catalyst degradation factor based at least partially on exhaust temperature increase event information.
 22. The method of claim 21, further comprising determining an overall SCR catalyst degradation factor by combining the first, second, and third SCR catalyst degradation factors.
 23. An exhaust aftertreatment system configured to receive an exhaust gas stream generated by an internal combustion engine, comprising: a selective catalytic reduction (SCR) catalyst; a reductant doser capable of being in reductant dosing communication with the exhaust gas stream upstream of the SCR catalyst; an SCR catalyst inlet NH₃ sensor upstream of the SCR catalyst and an SCR catalyst outlet NO_(x) sensor downstream of the SCR catalyst; and a controller communicable in electronic communication with the reductant doser to command the reductant doser to dose reductant into the exhaust gas stream, the controller comprising: a system properties modulation module configured to modulate an amount of NH₃ entering the SCR catalyst by commanding the reductant doser to inject reductant into the exhaust gas stream at a predefined flow rate; a system properties monitoring module configured to monitor an SCR catalyst inlet NH₃ signal generated by the SCR catalyst inlet NH₃ sensor and an SCR catalyst outlet NO_(x) signal generated by the SCR catalyst outlet NO_(x) sensor; a degradation factor module configured to compare a first time constant of the SCR catalyst inlet NH₃ signal and a second time constant of the SCR catalyst outlet NO_(x) signal, and further configured to determine an SCR catalyst degradation factor based at least partially on a difference between the first and second time constants; and a reductant doser module configured to determine a reductant dosing rate for achieving a desired exhaust emissions reduction based at least partially on the SCR catalyst degradation factor.
 24. The exhaust aftertreatment system of claim 23, wherein the SCR catalyst degradation factor is proportional to the difference between the first and second time constants.
 25. The exhaust aftertreatment system of claim 23, wherein the SCR catalyst degradation factor is a non-linear function of the difference between the first and second time constants. 